I haven't seen the movie, but it sounds like there might be more than one painting involved here.
The link Paul Clapham gave indicates (as does Wikipedia) that the painting that gets repainted every year is Luncheon of the Boating Party, which does include people eating lunch (duh) but I don't see an umbrella. And it doesn't seem to be composed of lots of little dots in primary colors.
In contrast, A Sunday Afternoon on the Island of La Grande Jatte does use lots of little dots, and has several umbrellas. I don't see anyone eating lunch though. No idea if this appeared in Amelie or not. Perhaps it did, and was discussed, but wasn't the painting that was being repainted?