PSG did look to be on course for a comfortable win against struggling opponents when Achraf Hakimi gave them a second-minute lead on a perishing evening at the Parc des Princes.
However, Matthis Abline equalised before half-time and the visitors then held on for a share of the points.
While Luis Enrique's PSG side toil in the Champions League and are in serious danger of a shock early exit from European competition, they remain undefeated this season in Ligue 1 and are now seven points clear at the top from Monaco.
However, the principality side will have the chance to close that gap when they play on Sunday away at third-placed Marseille.
Nantes, meanwhile, have now gone 10 matches without winning but they will see this as a precious point in their fight to avoid relegation.
"I think we put in a complete performance in that we dominated and created chances to score, in how we defended, but football rewards teams who score, not those who create chances," said Luis Enrique.
He said his team were "lacking a bit of confidence, clarity, precision and faith".
"It is frustrating, but all we can do is keep on insisting," he added, claiming it was "inexplicable" that his team failed to win a game in which they had so many more chances than their opponents.
That is a problem which has plagued them in the Champions League this season.
Luis Enrique made some notable selection decisions here with Portugal striker Goncalo Ramos leading the attack on his first start after more than three months on the sidelines with an ankle injury.
Gianluigi Donnarumma was recalled in goal after being controversially dropped in Munich, where the Russian Matfei Safonov was preferred to him but was at fault for the only goal of the game.
Sampaoli's first win
Ramos was involved as Paris went ahead inside two minutes, touching on a low cross from the left by Nuno Mendes for Hakimi to convert at the back post.
Lee Kang-in, preferred to Ousmane Dembele on the right wing, then struck the post as PSG pushed for a second goal.
Nantes offered little but they equalised against the run of play seven minutes before half-time as Abline got away from Willian Pacho before finishing past Donnarumma.
Abline came closer than anyone to scoring in the second half with a near-post header at a corner, as PSG dominated possession and territory but struggled to create clear scoring chances.
Earlier in France, former Argentina and Chile coach Jorge Sampaoli oversaw his first victory in charge of Rennes as Arnaud Kalimuendo scored a hat-trick in a 5-0 demolition of 10-man Saint-Etienne.
Kalimuendo, formerly of PSG, scored two of his goals from the penalty spot, while Ludovic Blas and Amine Gouiri also netted for a Rennes side who had lost their previous three matches.
The Brittany outfit, who appointed the ex-Marseille boss in early November after a poor start to the campaign, move up into mid-table thanks to the victory in Sampaoli's second match at the helm.
For Saint-Etienne, who were handicapped by the first-half sending-off of Mathieu Cafaro, the heavy loss leaves them two points clear of a Nantes team sitting in the relegation play-off place.
Meanwhile Brest bounced back from their 3-0 midweek loss to Barcelona in the Champions League with a 3-1 victory at home to Strasbourg.
© 2024 AFP