The surname Bunyan is derived from French, and some people speculate he's based on either Fabian Fournier or Bon Jean (or likely both), both French-Canadian lumberjacks.
(The other theory, of course, is that the whole fable is made up entirely to sell stories.)
In any case, Paul Bunyan (well, not the loli version) is often depicted dressed as the stereotypical French-Canadian (or French-New England) lumberjack anyway, so him (or her) being able to speak French is kinda expected.
All the time. Putting aside NNescio's stuff regarding the actual figure's background, FGO's Bunyan uses some simple French in her usual dialogue like saying tres bien as one of her victory lines.
As stated before Bunyan is French-American. She even says Enchante when she introduces herself to you and is actually one of the servants who speaks their native language the most out of the servants available I believe.
