Applications should be done on the registration website of the Paul Sabatier University. In particular the pre-registration procedure starts mid-March and ends mid-June (direct link to the preregistration page). After mid-June, you will be able to download the application folder, to fill it in and send it to the administrative office of the second year master.
Foreign students, should visit the Campus France website to see if a specific procedure applies to them.
For late applications, that is after mid-June, just contact the administrative office of the Master 2 degree.
In any case, it is important to send a detailled CV containing your grades and a description of your curriculum. Please also mention the Track of the M2R that you are most interested in (A: Pure math; B: PdP, modeling, scientific calculus, C: Probability and Statistics, or D: Bio-Math). The final choice of track will be done once the academic year has started.
If you have any difficulties with the registration website, do not hesitate to contact the administrative office of the second year master.