The learning of French, and some other modern European languages has long been a requirement of the British education system. Certainly until 20-30 years ago the learning of French was considered an absolute requirement for anything regarded as a proper education. Other languages, mainly German and Spanish are a very close second. However, that French is the traditionally learnt second language in British schools, and has been since proper education has existed, it is hardly surprising that the Royal Family are at least competent in French.

The english and british Kings are descendant of William the Conqueror, who become the first norman King of England in 1066 after defeating Harold II, the last Anglo-Saxon king.

As he was born and raised in Normandy, he would have been fluent in the french language spoken at the time.

He, his court, and the nobility continued to speak french afterwards (and it was considered the language of the elites, as opposed to english, the language of the conquered; here I am obviously referring to the old form of those languages).

The english Kings continued to have possession in present day France for another half millennium, at times claimed the throne of France, and actually briefly held it (under Henry V and Henry VI, in the second part of the hundred years war).

Later french become very important in all Europe, and it was the language normally used in diplomacy (it is still considered the "language of diplomacy" today; the treaties of Geneva are written in both english and french, many passports are issued in the language of the country and in french), and so a part of every good education.

Keeping in mind all of the above, I'd say that all thing considered it is quite possible that all english kings from William I onward spoke at least some french, and that the majority were certainly fluent.