Schachmann, a German who rides for Bora, edged two Belgians Dylan Teuns and Tiesj Benoot. Frenchman Julian Alaphilippe was three seconds back in fourth at the finish of a 154-kilometre loop that began and ended in Plaisir on the outskirts of Paris.
Schachmann collected a 10-second bonus for victory and the overall lead.
The opening day of the race, which went ahead while competitions in Italy were cancelled, was marked by preventive measures related to the coronavirus, including limiting contact with the riders for the public and the media.
"I planned to go to Italy but France has turned out pretty well," says Schachmann, who had been entered in the Tirreno-Adriatico stage race.
The Race to the Sun began in miserable northern French late winter weather. The rain made the course treacherous. Two of the French favourites, Warren Barguil and Romain Bardet suffered costly falls.
Bardet, who rides for AG2R Mondial, lost more than two minutes. Barguil, of Arkea-Samsic, was disqualified for slipstreaming the car of his team's sporting director Yvon Caer.
Alaphilippe, who rides for Deceuninck, and Benoot of Sunweb, were the last survivors of a group of 16 riders created when the pack split after a crash at a roundabout after 90 kilometres.
At 124 kilometres, Alaphilippe and Benoot escaped. The pack gave chase but only Schachmann and Teuns of Bahrain McLaren could catch them.
"On the last climb I went with Dylan and we bridged across. It was a crazy last corner but somehow I managed it," Schachmann said.
"It's my hardest race so far this season. I did not have great legs but in the end, I felt that in spite of the pain, I still had some strength left to make it back on the two leaders in the last stretch."
Bardet finished 2:42 behind the winner.
"A place in the top five has become difficult to envisage," said Vincent Lavenu, the head of the AG2R team, adding that there was a silver lining on a cloudy day. "In the tough stages, he will have more freedom. We're going to try for some individual exploits."
Caer and Barguil were fined.
"The rules and laws are there to be applied, but sometimes there is also the spirit," said Arkea team boss Emmanuel Hubert. "He was groggy after his fall and did not yet know which decision to take.
"The only aim was to help him recover his spirits and get him back in the race, if possible."
Schachmann, 26, won three stages of the Tour of the Basque Country last year. He finished second in the recent Tour of the Algarve in Portugal to Belgian Remco Evenepoel.
On Monday, the second stage heads south in a flat 166.5 kilometre run from Chevreuse to Chalette-sur-Loing that favours sprinters.
Results from the 154 km first stage of Paris-Nice from Plaisir to Plaisir on Sunday:
1. Maximilian Schachmann (GER/Bora) 3hr 32min 19sec, 2. Dylan Teuns (BEL/BAH) same time, 3. Tiesj Benoot (BEL/SUN) s.t., 4. Julian Alaphilippe (FRA/DEC) at 3sec, 5. Cees Bol (NED/SUN) 15 sec, 6. Nils Politt (GER/ISR) s.t., 7. Giacomo Nizzolo (ITA/NTT) s.t., 8. Sergio Higuita (COL/EF1) s.t., 9. Felix Grossschartner (AUT/BOR) s.t., 10. Yves Lampaert (BEL/DEC) s.t.
1. Maximilian Schachmann (GER/Bora) 3hr 32min 19sec, 2. Dylan Teuns (BEL/BAH) at 2sec, 3. Tiesj Benoot (BEL/SUN) 4sec, 4. Julian Alaphilippe (FRA/DEC) 7sec, 5. Pello Bilbao (ESP/BAH) 24sec, 6. Rudy Molard (FRA/FDJ) same time, 7. Cees Bol (NED/SUN) 25sec, 8. Nils Politt (GER/ISR) s.t., 9. Giacomo Nizzolo (ITA/NTT) s.t., 10. Sergio Higuita (COL/EF1) s.t.