This is a doable scenario. You can join a table twice in a query, usually assigning it a different alias to keep things straight.
For example:
SELECT s.name AS "student name", c1.className AS "student class", c2.className as "class list"
FROM s
JOIN many_to_many mtm ON s.id_student = mtm.id_student
JOIN c c1 ON s.id_class = c1.id_class
JOIN c c2 ON mtm.id_class = c2.id_class
This will give you a list of all students' names and "hardcoded" classes with all their classes from the many_to_many table.
That said, this schema doesn't make logical sense. From what I can gather, you want students to be able to have multiple classes, so the many_to_many table should be where you'd want to find the classes associated with a student. If the id_class entries used in table s are distinct from those in many_to_many (e.g., if s.id_class refers to, say, homeroom class assignments that only appear in that table while many_to_many.id_class refers to classes for credit and excludes homeroom classes), you're going to be better off splitting c into two tables instead.
If that's not the case, I have a hard time understanding why you'd want one class hardwired to the s table.
EDIT: Just saw your comment that this was a made-up schema to give an example. In other cases, this could be a sensible way to do things. For example, if you wanted to keep track of company locations, you might have a Company table, a Locations table, and a Countries table. The Company table might have a 1-many link to Countries where you would keep track of a company's headquarters country, but a many-to-many link through Locations where you keep track of every place the company has a store.
If you can give real information as to what the schema really represents for your client, it might be easier for us to figure out whether it's logical in this case or not.