Do you know companies focused on Rust where students can do internships? If possible in Madrid/Spain

I am a student from Madrid and I finish my DAM degree this year and I must start the internship and I would like to do it in a company where I can use the Rust language

I think you should not limit yourself to the Rust language to get internships. That said,

Have you tried linkedin? intern&location=European Union&origin=JOB_SEARCH_PAGE_SEARCH_BUTTON&refresh=true

From there you will see places that is offer engineering jobs. Try to find their home page and see if they have a place for job application, and see if they have internship programs.

I agree with the answer to not limit yourself, particularly early in your career. However, I recently read that the company formerly known as Twitter now called X wrote their AI assistant Grok in Rust. I can't comment on the company since I have no direct experience of it. (I also don't believe much that is written about it)