The girlfriend told a different story ... claiming Francois was the violent one, picking her up and throwing her to the ground in a jealous rage while she was 9 weeks pregnant.
Cops responded but couldn't determine who was telling the truth -- so no one was arrested. No charges were ever filed against Francois.
The 2nd incident went down in April when Francois was cited for marijuana possession in Tennessee -- after cops raided his home after receiving a tip Deondre may have been dealing weed out of the apartment.
Cops say Deondre tried to pin the weed they found on his girlfriend -- the same one from the domestic incident -- but they didn't believe him and cited the QB.
Despite the troubled offseason, Taggert still believes in the QB -- and will ride with him into the 2019 season.