La vieille dame et les pigeons (1998)

A starving gendarme, wasting away from hunger, is reduced to grabbing castoff snacks from fat American tourists. When he sees as old woman feeding pigeons, in desperation he hits on the bizarre idea of dressing up as one, replete with grotesque, oversized head, and passing himself off as one of them! She seems not to notice that he's a bit larger than her other birds - and it gets odder when he invites himself into her flat and gestures for her to make a meal for him. As the weeks pass, he gets fatter and fatter, and as he slips into his delusion, he starts believing he IS a pigeon. One day, he follows her to the kitchen, where he is shocked to discover that her real pet is another woman - dressed up as a cat! Then he realises she's just been fattening him up as a treat for the cat...