In addition to what everyone else has said the exact term you would use would depend on the country (or even different states within a country) since the education systems of USA/UK/Australia/Canada etc are different.
I believe in America (Americans might correct me) they are called magnet schools – public schools but with a certain specialisation. My family in Arizona sent their kids to a local school that has a particular emphasis on Spanish education. In the UK I think they have “specialist schools.”
So since the education systems are different there isn't one official name for this type of school. However if you said “a school which specialises in French” or “a school which has a particular emphasis on languages, like French” or similar it will sound natural and be understood.