Former Newcastle star Ginola was leaning against a studio desk along with fellow pundits Owen Hargreaves and Steve McManaman.
Presenter Humphrey, standing in front of the trio, made a light-hearted quip about the Frenchman's tatty-looking jeans and trainers, saying: "David clearly wasn't expecting to be seen full length."
Ginola, who spent seven years playing in England, responded with a resoundingly Anglo-Saxon hand gesture that was caught on camera as Hargreaves giggled like a schoolboy.
It's hard to imagine anyone being genuinely offended by such adolescent hijinks, but the broadcaster duly issued an apology via its Twitter account.
"BT Sport would like to apologise for any offence that was caused during this morning’s/Saturday’s broadcast," the broadcaster tweeted.
"David Ginola apologised straight afterwards as he realised this was an inappropriate action."
Last week ITV presenter Adrian Chiles had to apologise after making a light-hearted remark about Polish builders.
Match of the Day anchor Gary Lineker could be one to watch on Saturday night - on Friday he tweeted a picture of an infamous 'Jaegerbomb' drink, so the former England striker could be suffering something of an international hangover.