Cinderella is a fairy tale; it isn't based on a real historical event. The marriages of royal sons and daughters, from the beginnings of organized royalty as we understand the concept until it was no longer the case that absolute monarchy was the primary governmental system in most countries, were typically political affairs, especially of the heir to the throne. Alliances could be made or broken with a royal marriage, even to a less important prince or princess, and the marriages of the sons and daughters of reigning monarchs were generally arranged with great care to bring the best possible advantage to the kingdom.

I have not watched Ever After, but I will assume that the prince in question, like the prince in every other version of Cinderella I'm familiar with, is not mentioned to have any other siblings, and is the heir apparent of his father the king. In such a case---an only child, heir to the throne---there is absolutely no way that any monarch with any sense would simply invite a bunch of random young women to a ball in hopes that one of them might catch his fancy. An heir with no spare in the medieval era would have had his parents looking out for a potentially beneficial match from a very early age, and would very possibly have had one already arranged and ready to go well before he was old enough to actually marry.

It's possible that a younger royal son or daughter of a large family might have been allowed a spouse of their choosing, perhaps even one met at a ball or other social event, if the situation were such that there were enough alliances and potential alliances already on the table that the monarch could afford to be indulgent. Or, in the case that there were several potential matches, none of which stood out particularly strongly among the others as especially advantageous, the prince or princess whose marriage was in question might have been allowed to at least give an opinion on his or her preference. But a Cinderella situation, where a totally unknown young woman native to the country of the only-child heir to the throne in a time and place where absolute monarchy is the name of the game marries that heir, would not have happened. The only relevant historical event that I can think of which even slightly resembles it is the initially secret marriage of King Edward IV of England to Elizabeth Woodville, which ruined the possibility of either of the two potential alliance-marriages which were being negotiated for him at the time of this secret marriage. The political trouble arising from this was partially responsible for the beginning of the infamous Wars of the Roses, which is the kind of thing that arranged dynastic marriages are intended to prevent.