I would suggest yogurt rather than ricotta. What yogurt and creme France have in common is s similar acid content, which has implications for how well your cake rises.
Crème Fraiche
From Cook's Country | June/July 2007
"What is crème fraiche? If I can’t find it at my grocery store, can I use a substitute?
Créme fraiche, contrary to its English translation as "fresh cream," is actually heavy cream that has been soured with a bacterial culture. Texturally, it is similar to sour cream, but with a lighter, more refined flavor. Because crème fraiche will not curdle when boiled, it is often stirred into savory soups or sauces to add a lush finish. If your supermarket doesn't carry crème fraiche (or if you aren't willing to pay the hefty price), it can be made at home. Simply stir one tablespoon of cultured buttermilk into one cup of heavy cream, cover, and let sit at room temperature until the mixture has thickened (at least eight hours or up to two days). Refrigerated in an airtight container, homemade crème fraiche will keep for about two weeks. If you're in a pinch, whisking 2 tablespoons of heavy cream into 1 cup of sour cream will give you the correct flavor and texture, but if you're adding the mixture to a soup, be aware that it will separate if boiled."
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Crème Fraiche
From Cook's Country | June/July 2007
"What is crème fraiche? If I can’t find it at my grocery store, can I use a substitute?
Créme fraiche, contrary to its English translation as "fresh cream," is actually heavy cream that has been soured with a bacterial culture. Texturally, it is similar to sour cream, but with a lighter, more refined flavor. Because crème fraiche will not curdle when boiled, it is often stirred into savory soups or sauces to add a lush finish. If your supermarket doesn't carry crème fraiche (or if you aren't willing to pay the hefty price), it can be made at home. Simply stir one tablespoon of cultured buttermilk into one cup of heavy cream, cover, and let sit at room temperature until the mixture has thickened (at least eight hours or up to two days). Refrigerated in an airtight container, homemade crème fraiche will keep for about two weeks. If you're in a pinch, whisking 2 tablespoons of heavy cream into 1 cup of sour cream will give you the correct flavor and texture, but if you're adding the mixture to a soup, be aware that it will separate if boiled."