The snowfall was heaviest in the Massif Central mountain range, leading to 1,250 lorries and 200 cars blocked in traffic jams on Tuesday morning, according to the gendarmerie.
Provision of overnight accomodation "worked well", according to the minister responsible for cooperation with local authorities, Sébastein Lecornu.
800 vehicles jammed, 4,200 homes without power in Haute-Loire, France Info
Officials said that 1,100 people were placed in emergency accomodation and provided with food in the Haute-Loire and Loire départements.
Communist Senator Cécile Cukierman was not one of them.
She spent the night in her vehicle on the ringroad at the central city of Saint Etienne along with dozens of other motorists and slammed the "lack of humanity" of emergency services, whom she accused of being unprepared despite the weather forecasts.
Lorries had been left to become snowed in on steep roads, she claimed, echoing complaints from other car drivers.
Trees collapsed in snow in St Etienne, local radio reports
Further south, in the Aveyron, a 75-year-old woman was killed in a traffic accident caused by the weather.
Rail passengers stranded
There was trouble on the railways, too.
Some 500 passengers were stranded at Lyon's central station, when their train failed to run, 400 of them sleeping in the carriages and 100 being placed in hotels.
The SNCF rail company promised that the several services that have been disrupted would return to normal in the course of Monday morning.
Snow and ice orange alerts were lifted in eight départements but maintained in 17 on Tuesday morning.
Although only five were expected to be on alert by the afternoon, snow was forecast in Champagne, the Ardennes and the east of Ile de France.
Corsica badly hit
The Mediterranean island of Corsica was particularly badly hit, thanks to Storm Adrian.
A retired firefighter suffered a cracked skull when he was hit by a bit of a gate broken off by the wind, boats were overturned, seaside restauarants flooded and 25,000 households suffered power cuts on Monday night.
The storm moved north on Tuesday and a red alert, the first on southern Crosica's history and the second for the north of the island, was lifted.
Snow and rain have hit much of the rest of Europe, with 10 people dying from weather-related causes in Italy.