In France there are several mobile and internet providers. The four main actors are: Orange, Bouygues Telecom, SFR, and Free . You can walk into any of their stores (“boutique”) and in most places you should be able to get information in English.
In Monaco, the phone and internet provider is Monaco Telecom. There is a shop near IUM where you will get information in English.
To subscribe to any provider, you will need your identification document (ID card or passport), your local bank account information, and in many cases a document showing where you live “Justificatif de domicile”.