I mean of course a boat that would float and be able to reach a destination even if it is slow and hard to control. I understand having a fleet of smaller boats is way better, but I'm thinking about size only here (lenght, width, carrying capacity).
If the biggest possible boat was not in western Europe, I'm interested as well to know where it would be.
It's hard to say with confidence how big of a boat could have been built at that time. A lot depends on the design and the resources said king could have pulled together. At the time a large cog would be about 50 or 60 feet in length, and carry maybe up to 150 tons. Supposedly, there were some legendary viking longships that were up to 150 feet long, though those are not that well documented as far as I know. Try checking out: Gillian Hutchinson, Medieval Ships and Shipping
Disclaimer: I'm not a Medieval naval expert, though I do have some history in Medieval Mediterranean trade. If anyone has better information than I, please correct me.
Others will be able to answer this much better but without being able to speak for the other parts of the world, in China this was one of the golden ages of ship building.
The Quanzhou junk for example was an unearthed wrecked Junk from Song Dynasty (though slightly later than 1000 CE) with three masts and was over 114 ft. in length - meant to be about average size of sea-faring junks in the era. There were probably much larger ships as even 1000 years before this in the Han Dynasty four to seven mast junks were described by court historians. Joseph Needham in "Science and Civilization in China" describes that there were allegedly 12 mast junks in that era in the Song Dynasty, capable of carrying 1000 men each.