These are the ones you are most likely to see:
melon brodé: with a ‘netted’ rind, aka musk melon
melon Casaba: a yellow one with a wrinkly rind
melon jaune or melon canari: yellow rind and white flesh, ripe in summer but can last until December, hence its other name, melon d’hiver
melon miel: honeydew melon, with pale green flesh
melon sucrin: a greyish-purple melon with sweet orange flesh, also known as the Petit gris de Rennes
melon vert: melon with a dark green rind and pale green flesh, one of Les Treize Desserts.
Images by USDA photo by Scott Bauer. Image Number K7355-11., Yotoen