Chardy, who beat Federer at the Rome Masters earlier this month, spelled out why Djokovic is fancied to end eight-times champion Rafa Nadal's reign here.
Djokovic won seven of his nine break opportunities and fired down 31 winners as he eased into the third round.
"He was simply stronger than me, bigger than me in all compartments. You're always under pressure. He knows everything. He can do everything," said Chardy.
Roger Federer was kept on his toes before he eventually subdued Argentine journeyman Diego Sebastian Schwartzman 6-3 6-4 6-4 to reach the third round of the French Open on Wednesday.
The 17-times grand slam champion from Switzerland, was kept under pressure throughout by the world No. 109, who never gave up and even broke serve in the first set.
"I've always felt he had a little bit of an upper hand from the baseline. I feel he was doing a really good job being aggressive and making good plays," Federer, who next faces Russian Dmitry Tursunov, told a news conference.
"I wish I could have played a bit more freely today overall. But then again, I think it was a solid match.
"I served well. That's always the key to stay solid in your own service games."
Czech Tomas Berdych, the sixth seed, started slowly before beating Aleksandr Nedovyesov of Kazakhstan 6-7(4) 6-4 7-5 6-3.
Russian Mikhail Youzhny, the 15th seed, lost 6-0 6-3 3-6 6-4 to Czech Radek Stepanek before Spain's Marcel Granollers overturned a two-set deficit to beat 20th seed Alexandr Dologopolov of Ukraine 1-6 3-6 6-3 6-0 6-2.
Gilles Simon, the 29th seed, eased past Alejandro Gonzales of Colombia 6-4 6-0 6-2 and there were also straight-set wins for Spain's Roberto Bautista Agut, the 27th seed, and Ernests Gulbis, the 18th seed from Latvia.
French Open men's singles matches
2-Novak Djokovic (Serbia) beat Jeremy Chardy (France) 6-1 6-4 6-2
4-Roger Federer (Switzerland) beat Diego Schwartzman (Argentina) 6-3 6-4 6-4
6-Tomas Berdych (Czech Republic) beat Aleksandr Nedovyesov (Kazakhstan) 6-7(4) 6-4 7-5 6-3
8-Milos Raonic (Canada) beat Jiri Vesely (Czech Republic) 7-6(4) 6-4 6-1
13-Jo-Wilfried Tsonga (France) beat Jurgen Melzer (Austria) 6-2 6-3 6-4
Radek Stepanek (Czech Republic) beat 15-Mikhail Youzhny (Russia) 6-0 6-3 3-6 6-4
17-Tommy Robredo (Spain) beat Kenny De Schepper (France) 6-2 6-3 6-3
18-Ernests Gulbis (Latvia) beat Facundo Bagnis (Argentina) 6-2 7-5 6-0
Marcel Granollers (Spain) beat 20-Alexandr Dolgopolov (Ukraine) 1-6 3-6 6-3 6-0 6-2
22-Jerzy Janowicz (Poland) beat Jarkko Nieminen (Finland) 7-6(4) 7-6(4) 6-4
27-Roberto Bautista (Spain) beat Benoit Paire (France) 6-4 7-6(4) 6-2
29-Gilles Simon (France) beat Alejandro Gonzalez (Colombia) 6-4 6-0 6-2
31-Dmitry Tursunov (Russia) beat Sam Querrey (U.S.) 6-4 7-5 6-1
Martin Klizan (Slovakia) beat Robin Haase (Netherlands) 6-1 3-6 6-1 1-6 7-5
Steve Johnson (U.S.) beat Laurent Lokoli (France) 4-6 6-7(7) 7-6(3) 6-3 6-3
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