There are public structures that deal with psychiatric emergencies. They may be specialised in this field, but you can also go to the emergency room in French public hospitals: there is always a psychiatrist to deal with psychological cases.
In case of a physical emergency, you should always go to the emergency room of the nearest hospital and/or call the SAMU. The SAMU will be able to direct you to the appropriate structure(s) for the situation.
What you need: to facilitate the administrative process, you will be asked for your identity card, your health insurance card, your social security certificate and your health insurance card. But it is not an obligation to be taken care of.
Number to call: 15