We gave our American granddaughter residing in France $7,000 for tuition. Is this deductible?

You can take a tuition and fees deduction only for a dependent, so if your granddaughter is not your dependent, you’re out of luck. If she were your dependent, the deduction is capped at $4,000 (you must have income below a set limit) and applies only to an educational institution eligible to participate in a student aid program administered by the U.S. Department of Education. Studying abroad is not a problem as long as the school administering the program meets this requirement.