Ali Landry -- Pope Cops a Feel

The Pope's only been on the job a month ... and already he's getting touchy-feely.

Former Miss USA Ali Landry -- roughly six months pregnant with a baby boy -- visited the Vatican last week and got physical with Supreme Pontiff Pope Francis ... right in front of her husband!

OK, to be fair ... the Pope's hands-on tactics were a special blessing for Ali's unborn baby, and Vatican sources confirmed that.