Adrien Hunou stunned PSG in the first half by opening the scoring, but Mbappe would pull his side back into the match after scoring a second-half equaliser.
Neymar was shoved by team-mate Mbappe after PSG won the French equivalent of the Community Shield.
BARCELONA target Neymar must be allowed to leave PSG this summer.
In the 31st minute, PSG came close to levelling through defender Thilo Kehrer, but his headed effort got over the crossbar as the Ligue 1 champions went in search of a needed equalizer.
And the PSG players celebrated their success by posing for a team photo alongside the trophy, but Neymar was apparently getting in the way of the photo.
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The two came to the attention of police on July 19 when a pickup truck they used was found on fire in northern British Columbia. Police said earlier Tuesday they may now be driving a different vehicle and may have changed their appearances and clothing.
Coach Thomas Tuchel added that Neymar has trained well since returning for preseason and was involved in a group session ahead of the Rennes encounter despite the fact he is suspended following a clash with a supporter after their penalty shootout defeat in the Coupe de France final. Neymar moved from Barcelona to PSG in a world record fee two seasons ago and during his time at the Camp Nou, he scored 105 goals in 186 appearances for Barcelona.
Former Brazil player Edmilson said that after Barcelona star Lionel Messi will retire, Neymar can "very well" take the place of the Argentine player.
Mbappe spoke about his relationship with Neymar just yesterday, saying that he "admires and respects" Neymar and wants him to stay at the club. I have already spoken with him.
"The only thing I know is that I'll continue to give my all for Paris Saint-Germain, as after six years, Paris is my home and my family".
We don't know the full story - but this certainly doesn't look good. We had about 10 shots that somehow didn't go in. "I do not want him to leave".