Since 2015, french restaurants have the obligation to list the 17 major allergens present in their dishes (gluten/dairy/egg/fish/etc) for non-wrapped foods. In reality, the card is not always available.
Get the application "Avec Plaisir" it is an app designed to list allergen friendly restaurants. It's just a map with hearts beside the appropriate eating places:
(translate this page)
here is the app: https://play.google.com/store/apps/details?id=com.avecplaisir.avecplaisir&hl=en&gl=US
The law is called "décret n°2015-447 du 17 avril 2015"
You can contact restaurants first and ask them "J'aimerai manger chez vous, Pouvez vous SVP m'envoyer une liste des allergenes present dans vos plats, par mail ou MMS ou sur place? J'ai une allergie au lait.... Voici mon email... et mon Mobile:...."
There's lots of guides written in french already, search them on google and translate them:
apps, information, formus for people like you in France
You can help us by describing/getting a proper diagnosis for your condition, so that we can answer properly: Are you allergic to all cow's milk and goat's milk?
Cow milk allergies can be:
IgE-mediated cow’s milk allergy
Non-IgE-mediated cow’s milk allergy
Mixed allergic reaction
2/3% of babies have this, and only 0.4 of those keep it as adults.
I'd suggest that you photocopy a small card or an A5 print with an image of milk and cheese and a frowning smiley, with appropriate words, which I can't provide because you don't state any symptoms.
i.e.: "Bonjour, J'ai une allergie mortelle aux produits laitiers, s'il vous plait soyez en conscient, Merci"
And learn a spoken form of the same phrase which describes you specifically, i.e: "Bonjour, j'ai une allergie immunologoique sévere aux produits laitiers, s'il vous plait vérifiez de ne pas me nourrire de lait et de fromage, merci"
I would give you other examples of phrases pertaining to your condition in France if i had other info about your allergy.