Angers, the only team with a win so far, are the early leaders after the 2020-2021 started on Friday.
There were no Ligue 1 matches for five months as the 2019-2020 season was abandoned because of the COVID-19 crisis.
Dia outpaced Badiashile and beat Benjamin Lecomte with a low crossed shot in the fifth minute to give the visitors an early advantage.
The visitors doubled the tally 16 minutes later when Toure made the most of a defensive misunderstanding between Disasi and Badiashile.
Monaco, however, pulled one back on the stroke of halftime as Disasi headed home from point blank range.
The hosts equalised 10 minutes into the second half when Badiashile netted with an angled shot from Aleksandr Golovin's free kick.
PSG will face Bayern Munich in the Champions League final on Sunday.