Taxi unions have staged repeated demonstrations against Uber as debate rages in France over labour conditions for its drivers, who are mostly self-employed contractors with no job security.
Taxify, another app which started operations in the French capital last week, has vowed to undercut market leader Uber with backing from Chinese ride-sharing giant Didi Chuxin.
The FO-Capa VTC union said dozens of taxi drivers blocked Taxify's Paris recruitment offices on Monday afternoon.
"They have arrived in a shameful, aggressive manner," said union spokesman Helmi Mamlouk.
"We do not approve of them busting market prices, which are already pitiable."
The union notably opposes Taxify's offer of half-price rides in October, fearing it will take away business, according to a source close to Taxify's management.
Available in 19 countries in Central and Eastern Europe as well as Africa, Taxify operates like Uber via a smartphone app, allowing users to book rides and pay for them without using cash.
But the company says it will take only 15 percent commission from drivers, compared to Uber's 25 percent, and will price the rides 10 percent below the American giant.
"Paris is essentially dominated by one American company," Taxify's 23-year-old CEO Markus Villig told AFP last week.
"We want to prove that European companies can also come in and gain a significant market share and show some competition," said Villig, who founded Taxify when he was a 19-year old student.
Since launching their first protests against Uber's pricing policy two years ago, French drivers' unions and associations have repeatedly spoken out against the "pauperisation" of traditional cabbies.
The government of Socialist president Francois Hollande, who was replaced in May by centrist Emmanuel Macron, launched proceedings to put in place minimum pricing in the sector.