I last saw this one in the late 80s or early 90s so bear with me regarding details:
Most memorable scene:
A hilarious boxing match between the main character (Warren-Beatty-like cad, spiffy dresser, bit of a small-time criminal) and his likeable opponent (tall, bearded priest, bear of a man). Somewhere in a bar. They have their shoes nailed to the floor at arm's length from one another. They're both pretty sloshed. Every time one of them gets knocked over, the people behind them prop them back up.
Irish (?) priest is a Bud Spencer type character, I think in one scene he's making moonshine in the vestry.
Main character has a love interest who has a connection of some sort to the priest. But my memory has long blended parts of this film with "Irma la Douce".
Final scene: for all I know the film ends with a satisfying general riot, main character and priest on one side, baddies (other gangsters, police?) on the other.