Hartley was shown a yellow card by referee Ben Whitehouse on the half-hour mark as he was deemed to have made contact with Slimani at a ruck.
But a complaint has now been made by match citing commissioner, Douglas Hunter, and that means Hartley could be hit with a suspension.
The Saints hooker will now face a hearing in London on Wednesday.
Saints boss Jim Mallinder was asked about the incident after Saturday's game, which Saints lost 24-7 at Stade Marcel Michelin.
And Mallinder said: "When you come to a place like this in top level rugby, you need to be physical in your clear-outs, but you need to stay on your feet. You can't go diving off your feet and I think Dylan needed to stay up there rather than going on the ground.
"There was no intention there, it was just clear he should have stayed on his feet.
When asked if the sin-binning was a little harsh, Mallinder replied: "I think probably."