Have a regency until the king is normal again

Whatever would have happened to Jeoffrey, there would be a regency. 11 years old is too young to be king, so in any cases, there would have been a regency untill his majority.

Choose a regent that represent the king for the diplomatic visits and such, and make him rule alongside a council.

When he finally found true love, declare him major, and the regency can come to an end.

Regency was quite common, and was a good way to avoid chaos (wich lot of people want to avoid), so unless it last longer than few years, it will be accepted.

Edit: Here is a good article to show how common regencies were. You can also see how old the king were during the end of their regency, and constat that majority age was not a constant.
(thanks to aloisdg who link this wikipedia article)
List of regents on Wikipedia

Building on the excellent answers involving regency and grief, there's also that old trope: a body double.

In that time period there are no photographs or TV. Only the palace staff would even know what the child-king looked like, and they're, well, in on it.

Find an orphan (or maybe even a cousin) from another kingdom who looks more or less like the king looked before his transformation. Teach him a few basics and let him make an appearance when necessary.

An 11 year old monarch would be expected to appear at official events (like the opening of the town fair or the wedding of some top nobles) and to sit at court to learn, but not to actually make decisions yet. Given that his parents were murdered, it would be wise of the court to keep him mostly out of sight the rest of the time.

The Appeal

As the witch sought to leave, a brave young pushbrown blocked her way.

"Please, Lady Nimue," she pleaded, "If what you said is true, and you do this to teach our lord humility and kindness, pray consider this. What will happen to our land without her lord? At best, his vassals will do as they will. At worst, they will war with each other, trying to take the throne for themselves. So please, I ask you for a small reprieve. During the day... no, for just the afternoon, let the prince resume his true form, so that he may hold court and rule the kingdom."

The witch regarded the former chambermaid thoughtfully. Then her lips creased in a light smile.

"Very well," she agreed. Nimue gestured, and a wave of power passed over them, and settle into another part of the castle.

"In the western meeting room," she pronounced, "while the sun shines through the main window, the curse shall be eased. Any of you who enter the room during that time will regain your original forms. When you leave, or when the sun has fallen, your new shapes will be restored. And know that if you squander this reprieve, it will break. Use the room for any purpose but proper business, and the enchantment will be gone. And you will have to find another way to govern."

So saying, the enchantress vanished in a flurry of rose petals.

Magic must defeat magic

"Go," the prince growled, "Find me anyone. Any hedge magician, or alchemist, or illusionist. There must be another who can break this curse. Or at least find a way to disguise it."

So it was, after a few months search, that the wise old serving fork found the last true alchemist in the kingdom. And while his power and skill were not great enough to gainsay Nimue, lover and student of Merlin, he was able to brew a potion. It was slow to brew, and painful in effect. But it returned the prince to his rightful form for thirteen hours. But the potion itself was not without cost, if consumed more then once in a fortnight, it would tear the imbiber apart. Still, between the prince and his more trusted servants, they could try to keep the peace. It would have to be enough.

Spin Doctoring

"Good people," the cryer exclaimed, "Hear of our great woe. A powerful and arrogant witch set upon our beloved prince. She made sudden and terrible demands, and when our highness bravely refused her, she cursed not just the prince, but his entire court and castle. That curse has made it nigh impossible for the prince to keep court. So we beg of you, our people. Help to keep the kingdom alive, do your duties, and assist others. And if you hear tell of the witch Nimue, report it to the castle, immediately, that we might find her, and undo her magics."

The outcry was great, the people were united against a common foe. Though there were those who sought to take advantage, they were quickly found by the loyal. Or by the more shrewdly neutral. The crown was fractured, but the kingdom was stronger. After all, everything the bards reported was the truth. From a certain point of view.

Kingdom of Masks

Okay, no story blurb this time. But have the prince announce that none may see him, that he will hold court in an elaborate mask. And that all who come to call must also wear masks. Set the nobles against each other, seeing who can match the prince's elaborate and flawless disguise. Offer loaner visors to those who come to court without a mask.

One of the privileges of royalty is that they can be very exclusive of whom they allow in to see them.

The official story will be:

Jeoffrey is in seclusion and mourning the death of his parents, his missing staff were executed for allowing his parents, the king and queen to be murdered.

Guards are posted and given orders that no one shall enter or leave without express written permission. The guards themselves will pick up proclamations that will be delivered to them through a rotating message slot. (think revolving door but for messages/packages.

The proclamations will be then handed to the tax collectors, judges, et cetera, all authenticated by the existence of the royal seal. Eventually, a few trusted advisors will be allowed to meet with Jeoffrey personally, but only one at a time, so that there can never be collaborating witnesses.

Barons, Dukes and Counts, oh my!

If we're talking about monarchies, we're talking about feudalism, and if we're talking about feudalism, we're talking about layered bonds of liege and vassal.

If a select group of people can be informed about Jeoffrey's sudden monsterism, and I don't believe there isn't an answer that requires this in any case, then the path is straightforward: The Dukes, Counts royal, and Baronets are informed of the situation, and tasked with keeping business going as usual.

The notion that a king might meet with a peasant isn't absurd on the face of it; plenty of kings have held all sorts of audiences with all sorts of people, public and otherwise, but for a king to see no peasant whatsoever is also not absurd. An arrangement where the king only sees his court and his direct vassals is perfectly passable, at least for the relatively short timespan of 10 years that this involves.

In fact, the structures of a feudal society allows the king to keep taking petitions from his people, proxied through specially uplifted baronets or through his other vassals; and for him to keep answering petitions.

So TL;DR: The nested, hierarchical structure of feudal society makes a monarch in seclusion essentially a non-issue.

So if by any chance you are referring to "The Beauty And The Beast", the story was set in the 18th century. By the end of it (1789-99) the French revolution started and people simply began to "rule themselves". The forest village in the original story was also quite isolated so an absence of their prince might have been interpreted as "they fled the country" or "they have been killed".

"Taxes need to be collected, court needs to be held, land needs to be defended from barbarians.." And this all could and would still be done by electing actual democratic leaders.

He's transformed into a hideous beast? Great! Now he looks seriously aggressive – almost like how warriors dress in horned helmets and furs and the like.

So slap some armour round him, and make it look like he's just wearing armour with lots of fur and horns. Make up some rumour about how the young prince defeated with his own hands, the hideous beast that slew his parents. Now he's got an awesome story, to secure his rule.

Why doesn't he ever take the armour off? Some think perhaps he wears it continually as he's compensating for being young. Some think he's sensible to wear armour the whole time as a young prince is considered by some to be a weak target for a power-hungry lord. Some think it's because the beast's fur he wears is a reminder of his dearly loved parents.

King went to a war

Of course it's not that simple and the war lasting 10 years will be at least troublesome, moreover there will be a need of really trusted people around the king to keep that cover (of course the king will remain in country).

There are historical cases, when it was difficult to find out if the king is alive or not (and the king actually died). One example can be Polish and Hungarian king Wladyslaw III of Varna. It took 3 years before the new king took reign after Wladyslaw's death because of problems in establishing if the king actually died or not. And that's despite sultan showing king's head.

Most people never see a king. It's even less probable if the king is on a war. So you can keep the secret easily. The only problem will be with those really close to the king and those who have to hide the fact of king's absence in the battlefields. On the other hand when Suleiman the Great died, his death was hidden from soldiers for few days to prevent morale from plummeting (they were in a middle of a siege - successful by the way). If the war opens to more than one front line, it's easy to claim the king is either on his route between the lines or on the other line. A double can help to keep it quiet among the soldiers.

By conducting all business through musical dance numbers...

Music is akin to magic (or is it a form of innate magic? the magicians are still debating), and makes us see things which aren't strictly true. It may provide enough illusion to fool the eyes of the public.

And if anyone does get a good look, well, we all excuse some idiosyncrasies on the part of musicians, so it's probably just some flamboyant dress.