In order to apply for an internship in the United States, what exactly will I need to send? The academic transcripts of my grades? The TOEFL? The GRE? I'm a French student looking to do an internship in the United States.

My question is: in order to apply, what exactly will I need to send?

I'm guessing I'll need to send a CV and a resume... but what else?

Particularly, do I need to send the academic transcripts of my grades? (which are /20, so they're not in the same format as U.S. grades which are like A, B, C or D)

And also, I have the TOEFL and the GRE. Should I send them?
There is absolutely no "recipe" that anyone can give you, since every company will have its own expectations. Some may want just a résumé and a list of references; others may want your transcripts, a detailed CV, cover letter, and letters of reference; and still others may want something else instead.

You need to consult with the individual company's HR information.

(If you're talking about some sort of internship at a university, the same general rules apply.)