faire la sourde oreille

to deliberately ignore what someone is telling you

Used when someone hears a request or complaint perfectly well but chooses to act as if they hadn't, often to dodge an awkward answer.

Le voisin fait la sourde oreille à chaque fois qu'on lui parle du bruit.

The neighbour pretends not to hear every time we mention the noise.

Origin uncertain. The image is straightforward enough on its own, someone acting as if their hearing has failed rather than admit they are choosing not to listen.