Navalny and his brother Oleg were found guilty of fraud and money laundering via their transport and logistics firm which was working with Yves Rocher, one of the first foreign cosmetics brands to enter Russia in 1991, after the Soviet Union's demise.
Navalny was given a suspended sentence, but his brother was jailed for three-and-a-half years in what critics said was a politically-motivated case influenced by the government of Vladimir Putin.
Oleg Navalny was released last June.
Yves Rocher eventually acknowledged it had sustained "no damage" in 2014.
The cosmetics firm said in a statement sent to AFP on Tuesday that it had learned of the complaint "with surprise" and insisted that its Russian subsidiary had only applied "the usual procedures."
In 2017, the European Court of Human Rights denounced the Russian court for a ruling which was "arbitrary and manifestly unreasonable", ordering that the brothers be paid 83,000 euros ($93,000) in damages and costs.
The pair filed their lawsuit last year in Vannes, nor far from Yves Rocher's headquarters, and a judge was appointed to the case in February.
"We do believe that we will find here a real and fair justice which unfortunately we cannot find in Russia," Navalny said on Tuesday, speaking in English.
Navalny, who has long been one of Putin's most outspoken critics, has served repeated short jail sentences in connection with his political activities.