What a gorgeous name! I agree to keep the French spelling. Soleil looks SO elegant on paper.
My daughter's name is Eliette - also French, and for some reason VERY hard for people to pronounce. At least once a day I say, "You know, like Juliette, but Ellie."
And spelling? You can forget it. Elliette, Eliotte, Eliot, Elliott, I've seen it all! I had no idea this name was so tough for people.
It certainly would be easier if we named our kids Elizabeth or Sarah, but I love that our daughters' names are unique, feminine, and larger than our immediate cultural surroundings. I say go for it!