How do I approach this girl in my French class without being obvious?

I'm a first year college student taking French 101 with this girl I'm kind of interested in. I just don't know how to approach her and I feel like there's absolutely no reason for me to! She sits in the opposite side of the class in the opposite corner. Not only that, but my class gets split up into two groups: A and B. She's in A and I'm in B; there's absolutely no reason for anyone to talk to someone outside of their own group..

I found out that we have a lot of things in common (she's has said stuff in class, it's not like I stalked her), so I know there are so many possible things to talk about. My problem is that I just don't want her to automatically think I'm hitting on her and I'm not going to be weird about it at all.

Thanks in advance.