Once you have registered with a French doctor (see my post about “Déclaration de choix du médecin traitant” here) if you are unwell just call the doctor to arrange an appointment.
Here is what you need to say: “Je voudrais prendre rendez-vous, s’il vous plait”.
You should be able to see the doctor within 48 hours unless it is urgent he/she will be able to see you on the same day. Most doctors don’t have any flashy offices or receptionist. They take their own appointments (or their wives take the phone calls from home) so the first time you are visiting the doctor’s you might find it strange that no-one is there to greet you. Just wait in the waiting room (salle d’attente) until it is your turn. Some French doctors have open surgery so no appointment is needed. Just come when they are open!
At the end of the consultation, you will need to show your Carte Vitale and pay 22 euros. Most doctors take cheques or cash but they don’t take bank cards I guess to save on bank fees. Within a coupe of days 70% of the 22 euros will be reimbursed into your bank account from the French Social Security and if you have a top up insurance (Mutuelle) the 30% left will be covered.