Yes, I also agree with you that the game was very balanced, and it can be said that Nice won because they were lucky enough in this match. With this victory Nice can maintain their position at the top of the standings with only 1 point difference from Paris Saint Germain who are right below them.
Nice are also the only club unbeaten so far, but even so, there are still notes that they must improve, one of which is in their attack line. Because they have problems there, as evidenced by only being able to only create 10 goals from 9 matches they play.
Actually, Nice is above PSG, but this is not so important, at this stage there is only a two-point difference between PSG and Monaco and it is these three teams that will most likely get direct access to the Champions League. This season, France gets another place in the Champions League, which is a great achievement, and while Lille is in fourth place, I doubt that Brest will be able to move them up, and Marseille is still playing weakly enough, to lay claim to their place.
PSG have been able to improve their position considerably. After a few matches in the beginning of the season, PSG's position was from 5th to 6th in the points table and then we thought that maybe PSG will not be in a good position this season but due to their good performances in the last few matches they have been able to improve their points table considerably.
Monaco is number one in the points table with 20 points and PSG is in third position in the points table with 2 points less than them. The performance of PSG in the last few matches, if their consistency is maintained for most of the season, then it should not be difficult for PSG to recover these 2 points and go to the number one position in the points table. PSG will have to try to improve their performance from the current position they are in. If their performance deteriorates from this position, they could drop back to the bottom of the points table.