Racing on roads close to Bardet's hometown of Brioude, Froome was loudly booed as he chased to catch his GC rivals on the Col de Peyra Taillarde after suffering a mechanical on the approach to the first category climb.
"He is a champion and he deserves respect. I respect him as a rival and he does not deserve this sort of treatment."
Watch: Tour de France stage 15 highlights
Racing through Bardet's home department of Haute-Loire, Ag2r La Mondiale were expected to ride an aggressive race on stage 15, hitting the front of the group of favourites as the race approached the stage's final first category climb.
As the pace went up Froome suffered a problem with his rear wheel, and despite a quick change with team-mate Michal Kwiatkowski, had a long chase to rejoin his rivals for the yellow jersey.
The boos from the crowd were loud and clear as Froome chased back on, although when asked about them at the finish the Team Sky rider said he was unconcerned by his reception, saying that it was "expected" from a passionate home crowd.
The Tour de France continues on Tuesday, with stage 16 starting in the same town which hosted the finish of stage 15, before heading east towards a flat finish in Romans-sur-Isère.
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