It is not at all uncommon for lycée students to board, especially if they want to follow a course that is not available locally. French parents also put their children into the internat – even if the school is not very far away – in the hope that they will work harder.
There is often supervised homework in the evenings, for example, and computer (and TV) use is restricted. (At my daughter's internat, although computers are available to the boarders, they are not allowed onto facebook which gives her hours of extra study time!)
The internat, however, is a far cry from a British (public) boarding school in terms of facilities. Rooms are functional – students may or may not share – and if they get sick they are sent home. You provide their bedlinen etc., and they bring their washing home at weekends.
However, supervision is good and there are often evening clubs - film, photography, etc. to entertain the boarders. Children stay either Sunday or Monday night to Friday afternoon and the internat is closed at weekends.
The education is, of course, free in state internats and the boarding costs are around 1200€ a year, with grants available if your income is low and your child is a boursier (more on being a boursier here). There are also grants towards traveling costs – as long as your child is attending the nearest lycée offering their chosen course.