Am I secretly British?

So apparently I speak French with a British accent...funny, huh? Since I've been in France, people have always asked me right away if I'm British...and I always thought it was just because the American and British accents come out about the same in French. But the other day I found out that there is a reason why people always think I'm British. Apparently the accents are completely different, and mine is not American...explain that one! I was sitting chatting with the parents of the kids I take care of, and they were like, "You know, you have a British accent." They've said this to me before, so I didn't think much of it. Then they say, "Really. We would say for sure that you are British, not American." I wasn't sure how to feel about that. From what I can tell, the French don't have the highest opinion of the British. It seems to me that they like Americans better. In any case, it's fun to surprise people by telling them that I'm actually from the other side of the pond...