That is correct, and Richard III might then be called the last English king, except he was king of both England and Wales. George II was German, but ruled Britain, and likewise, the current owners of the British crown, the Windsors of Saxe-Coburg and Gotha, are also German. Sort of.
But then again, one could also say that the Plantagenets, including Richard III, were French, of the house of the Angevin Counts of Anjou.
Yes, certainly the Plantagenets had strong ties to France by blood. Plantagenet is a French name (it means “broom”). Richard the Third spoke fluent French.