We generally discourage mixed backgrounds for a first character, partly because we expect the background to be fully explained in the character history (as opposed to "X moved to France because she liked it where she met Y and they got married"). However, more importantly, what does having a mixed background give your character that they couldn't have by being simply French or English?
So yes, it is possible, but it's going to take more work to get the character sorted than if you go for a single nationality. If you are determined though, I recommend that you work on your character in the
Sandbox and meet other members at the same time (actually it's a good idea to do this anyway

)
Welcome to Magical Hogwarts!
[carys]~ Carys