Son histoire ne tient pas debout.
saw nee-stwaar nuh teeYAA pah duh-BOO. Click below to hear this.*
His story doesn’t hold water.
First off, let’s clarify that it could just as well be her story. Without a context, the French doesn’t allow us to determine who’s telling all these lies. We’ll just say “his” for simplicity’s sake.
In English, his story is a bucket full of holes. It doesn’t hold water is a nice picturesque way of saying that the story is so full of holes that it’s useless and without truth. In French, his story is a three-legged stool with two legs: It doesn’t stand up.
Either way, if this were a TV detective series, that suspect would be in the interview room with those cops for a long, long time. He needs to read Sir Walter Scott (no, it wasn’t Shakespeare who said this!):
Oh, what a tangled web we weave,
When first we practice to deceive!
*Some mobile phones, such as Blackberries, won’t display the audio player. If no player appears, here’s an alternative link to the audio file: