I will try to answer all of your questions to the best of my knowledge. First, however, understand that until you have an actual LSAT score this is all speculation. The LSAT is such an important part of obtaining scholarships and admissions that without a score it is hard to do much more than guess.
How the scholarship system works for international applicant ?
I think it works the same as for a U.S. student. You simply apply to schools, and they will offer scholarships based primarily on your GPA and LSAT. There may be some special applications required for international students of which I am unaware. Check with each individual law school to find out.
Is it possible for an international applicant to have scholarships that cover the entire tuition and fee ?
Yes, but again it depends on your GPA and LSAT score. The higher your numbers, the better chance you have of obtaining a full scholarship. You may also be able to apply for specific scholarships for international students or scholarships from private organizations.
If I apply to a law school requiring an LSAT score that is actually below the score i'll have, can i get a better scholarship ?
Generally speaking, yes. The amount of scholarship you receive, however, will depend on how far above the school's average score you are. For example, let's say you score 160 and apply to a school with an average LSAT score of 147. You would likely receive a very large scholarship, maybe a full scholarship. If you apply to a school with an average of 155, you will likely receive some scholarships, but not a full scholarship.
If you score around 150 it will be difficult to get a full scholarship. There may some schools that will offer one, but they will be smaller, lower ranked schools. This leads me to my next point:
It is fine to go to a lower ranked school as long as you understand the possible limitations of the degree. I don't know if you plan to move back to France after school or to stay in the U.S., but most graduates of these schools will find work in the immediate location of the school. So, if you go to a lower ranked school in San Diego it would be very difficult to then move to New York or Washington D.C. and to find a job. It may also be difficult to move back to France, since no one will have heard of the school.
Do you know what you want to do with the degree? Where you want to practice?