The travel disruption goes beyond the roads; over 700 passengers were stuck and given shelter in the Montparnasse and Austerlitz stations overnight last night, and over 600 people needed to be given shelter in Paris homeless shelters too, due to being stranded by the snow.
Several tram and commuter rail lines shut down completely, and nearly all bus services were halted.
They managed to get in about an hour of runs on Wednesday morning on the slopes of the park that descends from the church, as well as on some nearby streets, before being chased off by the police.
Tourists in the City of Lights found the Eiffel Tower closed for a second day, while the capital's airports were hit with delays and cancellations.
The weather caused major gridlock across the city, with more than 700km (430 miles) of traffic jams recorded at 7.30pm local time (1830 GMT) on Tuesday, local information service Sytadin said.
"It's attractive when it snows".
"It's a natural event, but it's not normal because they leave all the roads blocked, without salting them" to remove the ice, he said.
Transport conditions have prompted the Interior Minister's office to request that people not use their cars in any snow-affected areas, except where absolutely necessary.
"I didn't sleep at all", said Rodrigue Akpadji, a German teacher who works in Saclay in the southern Paris suburbs, as the tailbacks continued to stretch 200 km on Wednesday morning.
The greater Paris region is among 27 departments that have been placed under alert across the country, according to Meteo France.
Many travellers were stuck at the airport as train services resumed only slowly after being halted early Wednesday, and few taxis were willing to courageous the roads.
Men walk with skis on a snow-covered path near the Eiffel Tower in Paris, as winter weather with snow and freezing temperatures arrive in France.
Several flights from Paris airports were cancelled or delayed. "I love Paris. I would just love to get there and see it".