OK folks, thank you for the mostly constructive replies.
I found the following from a vegetarian website, so unless anyone thinks it's wrong I'll try and use that
Je suis vegan (végétalienne). Je mange que des vegetables, cereals et grains. Je ne mange pas des produits animaux, ni du miel, ouefs ou laitage et ses dérivés. Pouvez-vouz m'aider à choisir dans votre menu ? S'il vous plaît, alertais-moi si un repas, sauce ou garniture à ces ingredients. - I'm vegan. I only eat vegetables, cereals and grains. I don't eat any animal products, neither honey, eggs nor dairy and its derivatives. Can you assist me in making my choice from your menu? Please, alert me if a food, sauce or garnish contains these ingredients.
Je suis un végétarien(ne). Je ne mange pas de viande, de porc ou de poulet - I am a vegetarian(female). I do not eat meat, pork or chicken
Je ne mange pas d'œufs, du lait ni de fromage - I do not eat eggs, milk or cheese
Végétalien(ne) - vegan
The bit I totally don't get is the masculine/feminine thing, but that's clearly going to be the least of my worries.
As for Muckdonald's it's academic, as I wouldn't be seen dead in there anyway.