Russia's Foreign Ministry summoned French Ambassador Jean-Maurice Ripert on Wednesday to complain about the "discriminatory character" of the recent detainment of dozens of Russian football fans.
The European Championship in France has been marred by violence caused by supporters and on Wednesday police were forced to use tear gas against hundreds of England fans in the city of Lille, where Russia supporters were also gathered.
Russia and England fans previously clashed in Marseille before and after Saturday's 1-1 draw and governing body UEFA said Russia would be ejected from the tournament in case of any repeat inside a stadium.
The Russian Foreign Ministry said 43 people were taken into custody by French authorities while heading from Marseille to Lille and were ordered to be detained for a period of 48 hours.
"Further anti-Russian sentiment regarding our national team's participation in the European football championship has the power to substantially harm Russian-French relations," the ministry said in a statement on its website.
On Wednesday, Russia lost 2-1 against Slovakia in Lille but there was no violence in the stadium, although one flare was lit by Russian fans.
The local region's police prefect, Michel Lalande, said in a statement that 16 people had been arrested on Wednesday in total, including six Russians implicated in last Saturday's violence in Marseille.
A train from London en route to Lille was also stopped and five people were arrested for being drunk and disorderly. Alcohol restrictions are in force in the city.
The statement also said the hundreds of England fans were "dispersed without incident" by police.
A dpa witness said police had used pepper spray and batons as well as tear gas to deal with the England supporters, who had been singing anti-Russian songs and throwing beer bottles. The situation had however calmed down.
Several senior Russian officials have publicly supported the country's fans, but Kremlin spokesman Dmitry Peskov has condemned the violence and said President Vladimir Putin did not agree with the other officials.
Russia's Sports Minister Vitaly Mutko, who is also the acting head of the Russian Football Union, on Tuesday backed Russian fans.
"Our fans are being constantly provoked," Mutko said in comments carried by state news agency TASS. "There is no guarantee that the disturbances will not happen again."
Igor Lebedev, a member of the Russian Football Union's executive committee and a vice speaker of Russia's parliament, egged on the violent fans on his Twitter page.
"I don't see anything terrible in the fans' fight. On the contrary, our guys did a good job. Keep it up!" Lebedev said.
Vladimir Markin, spokesman for Russia's federal Investigative Committee, said Europeans were "surprised to see a real man as he should be" because "they are used to seeing 'men' only at gay parades."
The clashes over the weekend in Marseille left at least 35 people injured.
Marseille prosecutor Brice Robin called the Russian hooligans "highly trained" and organized, saying they posed a serious risk. Not one person of the group, estimated by Robin to be about 150 people, was arrested by French police.
The violence could jeopardize the number of potential foreign visitors to the 2018 football World Cup being hosted by Russia. The country is spending an estimated 10 billion euros (11 billion dollars) on the tournament.
England fans are in Lille ahead of their Group B match with Wales on Thursday in the nearby smaller city of Lens.