There's a school in France ( well at least two I think ) that teach videogame design, or something. Supinfogames in northern France and ... And something else, I'll have to ask a colleague of mine who was in the second.
Supinfogames was created some time ago, when I was myself in the "original" school of the group. I think it somehow evolved in something viable nowdays. I'm not sure. I don't think drawing was a prerequisite though : I did an artsy school myself and I don't know to draw for sh!t.
Bottom line : don't dismiss yourself unless you tried really hard. And even then, still don't dismiss yourself. ( hint : I do. I hate wasting time. =) )