Attacking midfielder Rony Lopes got the opener, heading a deflected cross past Nantes goalkeeper Ciprian Tatarusanu in the 69th minute. Falcao's clever flick then helped fellow striker Stevan Jovetic double the lead 10 minutes from time.
Colombia international Falcao rounded off the scoring by running on to Samuel Grandsir's pass and neatly finishing in the 82nd minute. Nantes substitute Emiliano Sala pulled one back for the hosts in added time.
Newly-promoted Nimes Olympique marked their first top-flight match for 25 years with a comeback victory over Angers in a seven-goal thriller.
Nimes forward Clement Depres scored a brace while Sada Thioub and Renaud Ripart also found the net to cancel out strikes by Pierrick Capelle, Angelo Fulgini and Ismael Traore.
Former France and Arsenal midfielder Patrick Vieira began his career in charge of Nice with a tame 1-0 defeat by Stade Reims. Nice never recovered from Malian winger Moussa Doumbia's third minute goal.
St Etienne needed a late goal from French forward Lois Diony to seal a 2-1 victory over Guingamp. Wahbi Khazri had given 10-times Ligue 1 champions St Etienne the lead in the 45th minute before Guingamp equalised through Marcus Thuram, the son of former France defender Lilian Thuram.
Lille powered past Stade Rennais 3-1 while Dijon too began with a win by seeing off Montpellier 2-1.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar)
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