Colombian striker Falcao, who joined Monaco from Atletico Madrid in May last year, left the principality club to join Manchester United on a season-long loan deal believed to be worth £6miillion.
United have an option to buy the 28-year-old for a rumoured €55million (£43.5m), with the switch acting as further evidence that Monaco's hopes of becoming a European force are set to come to an end.
Monaco also loaned defender Nicolas Isimat-Mirin to Dutch club PSV, while young PSG forward Hervin Ongenda will spend the rest of the season on loan at Bastia, who also brought in striker Benjamin Mokulu on loan from Mechelen.
Monaco and PSG were not the only teams to lose players on deadline day, with Montpellier and Lorient – who signed midfielder Francois Bellugou from Nancy - both seeing key members of their squad depart.
Montpellier sold midfielder Benjamin Stambouli to Tottenham Hotspur and Lorient defender Bruno Ecuele Manga made the move to Cardiff City.
Marseille were arguably the biggest French club to do incoming business as Marcelo Bielsa made his fourth signing of the transfer window by bringing in 19-year-old Brazilian centre-back Doria from Botafogo.
Meanwhile wingers Foued Kadir and Morgan Amalfitano both departed the Velodrome, Kadir moving to Betis on a season-long loan and Amalfitano making the switch to West Ham.
Lille found their replacement for Salomon Kalou, who joined Hertha Berlin on Sunday, by recruiting Swiss striker Michael Frey from Young Boys on a four-year deal.
Reims were one of the busier clubs on the last day of the transfer window as they bolstered their attacking options with the acquisition of striker David N'Gog on a two-year deal and the loan capture of full-back Valentin Roberge from Sunderland.
Guingamp saw their top scorer last season depart as Mustapha Yatabare left for Trabzonspor, but his brother Sambou Yatabare joined the Brittany club on loan from Olympiacos.
Elsewhere, Evian – who have taken just one point from their first four Ligue 1 games – boosted a backline that has shipped 10 goals so far by acquiring former Monaco and Marseille defender Gael Givet on a two-year-contract