I have an F-1 Visa but I will not attend the university because I couldn't get an scholarship. Instead I will attend a university at France. Could I use my F-1 visa to enter the US to make a connection flight? Would it be valid?
No. An F-1 visa is valid for study. You can only use it to enter the US when you are properly enrolled at an authorized institution and they have indicated this status in the SEVIS database. When you arrive at the port of entry, the officer will check the database and you may well be denied entry.
If your nationality is such that you need a visa to transit the United States, you'll need to apply for a new visa.