The UberPOP app was ruled illegal by the French government last year, but the company hasn't yet exhausted all legal recourse.
Didier Hogrel, president of the National Federation of Taxis, told CNN that the taxi drivers were taking action at Paris' airports, at the capital's Gare du Nord and Gare de Lyon train stations, and at Porte Maillot, in the Montparnasse area.
One taxi driver was injured by a private car driver near Orly airport Thursday morning and was taken to a hospital, he said.
U.S. singer Courtney Love said she had been caught up in the protests, tweeting, "they've ambushed our car and are holding our driver hostage. they're beating the cars with metal bats. this is France?? I'm safer in Baghdad."
Love, who said her car had been attacked after leaving the airport, later tweeted that she had "got out after being held hostage for an hour" thanks to two motorcycle riders.
And she angrily called on French President Francois Hollande to act, saying, "Is it legal for your people to attack visitors?"
At Gare du Nord, when British business travelers Hardy Blechman and David Keogh arrived for their flight, their Uber car came with a baseball bat.
"Our first driver sped away as taxi drivers approached us loading his cab. Our second driver agreed to meet us in a back street near Gare du Nord and passed David a baseball bat to hold," Blechman said
"Passengers aren't the target, but I would be extremely scared if I was an Uber driver."
Uber: Small minority are protesting
Police told CNN's French affiliate BFMTV that 2,800 taxi drivers were protesting across the country.
Uber said the number was smaller. Uber spokesman Thomas Meister told CNN: "There's 50,000 taxis in France, only roughly 1,000 are demonstrating today and the violence is just unacceptable.
"We're talking about a small minority, totally reluctant to (accept) any sort of change."
UberPOP, which operates in more than a dozen cities across Europe, gives passengers a cheaper alternative to traditional taxis by letting private drivers offer rides.
But the fact that these drivers are not licensed doesn't sit well with established taxi firms and local officials.
Video footage from Paris showed riot police on the streets Thursday, as well as tires set on fire and vehicles apparently overturned.
Access to Charles de Gaulle and Orly airports was disrupted for several hours, police said. Protesting taxi drivers also slowed down traffic on the A13 freeway, heading northwest out of the capital.
Police urged people trying to reach Paris' airports to take the train or metro rather than travel by road.
By Thursday night, taxi drivers had gathered at Porte Maillot near the Champs Elysees.
"We are tired of this situation," said Alain Griset, president of the National Union of Taxi Drivers. "This will go on indefinitely, at least tonight and tomorrow."
Minister calls for decree banning UberPOP
Further French court rulings on UberPOP are still expected.
Uber insists that its activities in France are legal. "Under the rule of law, the justice is in charge of determining what is legal and what is illegal; so far no French court of justice has declared POP illegal and asked us to stop operations," Meister said.
However, Interior Minister Bernard Cazeneuve, speaking on BFMTV Thursday, reiterated the French government's position that UberPOP is illegal under industry laws passed last year.
Cazeneuve said he had asked the Paris police authority to issue a decree banning UberPOP. Similar decrees have already been issued in other major French cities.
Hogrel, of the National Federation of Taxis, said taxi representatives were due to meet with government officials on Thursday.
He called for authorities to ban the UberPOP app, thus preventing users from accessing the service online, saying: "We can't put a cop behind each citizen using his car."
But Cazeneuve told BFMTV that an app could only be banned following a court order.
Following the meeting, Cazeneuve said vehicles using UberPOP will now "be systematically seized" by police when caught operating.
Meister, Uber's spokesman, said the company is "still assessing on which legal ground such measures could be implemented."
'Nothing justifies acts of violence'
On Tuesday, Cazeneuve urged calm on all sides in a statement issued as tensions simmered between taxi drivers and UberPOP drivers.
The law must be respected, he said, and "nothing justifies acts of violence."
According to the law, Cazeneuve said, UberPOP is illegal and its drivers risk prison terms and the confiscation of their vehicles. Some have already had such penalties imposed, he said.
Whatever UberPOP argues, Cazeneuve said, its drivers are not paying taxes or charges and are in effect working in the black market.
UberPOP users should also be aware that they run a risk by using drivers who aren't professionals and aren't insured to carry fare-paying passengers, he said.