In the French education system, what is the difference between doctorant ("PhD student") and doctorant contractuel ("contractual PhD Student")?
In France (like other countries), there are several ways to fund a PhD student.
A doctorant contractuel is a legal designation used to refer to someone who has signed a specific job contract called a contrat doctoral. This contracts allows universities to hire PhD students and describes the working conditions of the PhD student as an employee of said university.
Note that, in addition to this contract, a decree (2009-464 in the Wiki link) can also modify the working conditions by stating that a PhD student funded with such a contract must spend 100% of his/her time on research activities. As a result, an additional clause must be signed to be allowed to do teaching activities. From what I know, this is the one crucial point to be aware of when proposing or signing such a contract.
A doctorant is a just a term used to designate a PhD student, without any distinction regarding the nature and source of the funding.