Quoting LiveLove2012(::" Both are correct spellings. Clare is Irish and Claire is French. Another correct variation is Clair."
Quoting Back to Noob Status:" Clair reminds me of Clair de Lune. <3"I didn't even think of that! My grandmother is full French and she use to sing "Au Clair De La Lune" to me all the time. I sang it in high school for my regional auditions. The first half I did in French, the second in English. I ALMOST made regionals! I was 2 points off lol