The confrontation came as teams jostled for position at the end of a relatively flat journey that suited sprint specialists within the peleton.
Bauer's job is to deliver Quick-Step speedster Marcel Kittel to the front of the field and Kittel's four stage wins so far suggest Bauer is doing a great job.
"Because the finale is so technical, positioning is so key and speeds are so high approaching the final three kilometres," reflected Bauer, 32, afterwards.
"When you come to a finale like today, if you're out of position, you're not really making it up without a huge effort. If you have to make a huge effort that distance from the line, you're not going to sprint for the win."
Bauer's exchange with Bouhanni, 26, came about seven kilometres from home, as the Quick-Step team began their drive to the front, perhaps nudging the Frenchman out of their path in the process.
Bouhanni would finish sixth in Kittel's wake, with Bauer 25th and 126th overall.
But it's not the first time Bouhanni's temper has got the better of him - he missed last year's French championship and Tour de France, after breaking his hand in an altercation with hotel guests.
"I'll stop cycling around 32 years of age and that will leave me at least two years to go as high as I can in boxing," he told L'Équipe magazine in 2014. "Just like as a cyclist, I'll be 100 percent invested in it.
"Boxing is my passion and cycling is my job."
And Bauer also has a reputation as one of cycling's toughest hombres. His 2013 Tour debut ended early, when he left the road at high speed and ploughed through a wire fence, suffering gruesome facial injuries.
The following year, he returned to so nearly capture a stage win, when he was part of a two-man breakaway that led for more than 200km, but was gobbled up by the peleton 75 metres from the finish.
With 11 stages remaining on this Tour, he looms as a key figure in Kittel's quest for the points title.
"He's obviously on a roll - his confidence is probably on an all-time high - and it's great to be part of," said Bauer.
"[Kittel] is a legend, very relaxed both on the bike and off the bike, but inside the last 3km, he changes ... he becomes a bit of a bull.
"There are a few more sprint opportunities and we expect we can deliver again in coming days."
Englishman Chris Froome leads the general classification by 18 seconds, from Italian Fabio Aru, with Frenchman Romain Bardet third.
Kiwi George Bennett retains 10th overall, three minutes 53 seconds behind Froome.
