Monaco virtually made sure of their French Ligue 1 survival with a 2-0 win over Amiens on Saturday while champions PSG signed off their home campaign with Kylian Mbappe scoring his 32nd league goal of the season in a 4-0 win over Dijon.
Falcao and Alexander Golovin scored in either half at the Stade Louis II to take Monaco to 36 points and three above the drop zone with one match left to play.
Monaco, the 2017 champions, are not mathematically safe but they have a three-point lead over Caen who occupy the relegation play-off spot with a goal difference of seven.
Guingamp were already relegated. Dijon joined them in the second division for next season when they lost 4-0 at PSG.
French World Cup winner Mbappe, back from a three-match ban for a red card in the French Cup final, scored two of the goals to take his league tally to 32 with one game left.
He is the first French player to reach that figure since Herve Revelli scored 31 for Saint-Etienne in the 1966/67 season.
Elsewhere, Lille made sure of second place and a spot in the Champions League group stages with a 5-0 rout of Angers.
Nicolas Pepe, who will leave the club in the summer, scored twice to take his season tally to 22.
Lyon will finish third — enough for a Champions League preliminary round place — after a 3-0 win over Nice.