This is the Argentine striker's seventh career award.
Manchester United forward Cristiano Ronaldo finished sixth in the voting.
Top 5 include Robert Lewandowski (Bayern Munich), Jorginho (Chelsea), Karim Benzema (Real Madrid), N'Golo Kante (Chelsea).
Lewandowski was named the best forward of the year.
This is the first time a French publication has presented this award.
The prize goes to the player who has scored the most goals for the club and national team in a calendar year.
Lewandowski has scored 64 goals this year for Bayern Munich and the Polish national team.
Borneo Spain and Barcelona midfielder Pedri was named the best young footballer of the year.
The best footballer of the year was Barcelona midfielder Alexia Putellas.
Paris Saint-Germain goalkeeper Gianluigi Donnarumma was named the best goalkeeper.
The 22-year-old European champion received the Lev Yashin prize.
Chelsea are France Football's Best Team of 2021.
Earlier, Manchester United forward Cristiano Ronaldo said that France Football magazine editor-in-chief Pascal Ferret was deceiving his readers.