Documents filed with US regulator said French authorities recently completed an audit of Booking.com's accounts from 2003 to 2012.
The French government said Booking.com had a base in France and was obliged to pay income and value-added taxes.
The company said the majority of funds being sought are penalties.
"In December 2015, the French tax authorities issued Booking.com assessments for approximately €356m, the majority of which would represent penalties and interest," the filing with the Securities and Exchange Commission said.
The company said believed it complied with local tax law, and would contest the ruling in court if it could not reach a settlement with the French government.
In the same filing Priceline said Italian tax authorities were examining "whether Booking.com should be subject to additional tax obligations in Italy".
Last week, Google's headquarters in Paris were searched as part of an investigation into possible tax evasion.

Highlands and Islands Fire and Rescue Service recorded the acreage of several of the most serious of the 73 heath and grass fires its crews have tackled.
The 332-acre total includes 100 acres burnt in Locaber on 1 May, but does not take into account all land affected.
Landowners contributed more than Â£1m towards the cost of the fire fighting.
The Scottish Rural Property and Business Association (SRPBA), which has provided the figure, said private landowners and estates supplied staff, specialist equipment and paid for helicopters to water-bomb flames.
Highlands and Islands Fire and Rescue Service (HIFRS) said the majority of wild fires in its area were now out.
Parts of Aberdeenshire, Argyll and Fife were also affected during a dry and windy spell of weather.
Crews tackled flames on the Balmoral Estate in Aberdeenshire, while smoke from a fire near Tyndrum temporarily closed the A82 in Argyll.
The north-west Highlands was the worst hit.
Since the start of the month, 150 acres of burning heath were tackled by crews from Fort William, Newtonmore and Kilchoan.
Acharacle and Mallaig dealt with a 100-acre heath fire, while crews from Stornoway and South Lochs extinguished a 24-acre grass fire on Lewis.
Dunvegan, Portree and Uig crews extinguished a wild fire that burnt 40 acres on Skye.
Hampden Park in Glasgow, Scotland's national stadium, sits in 33 acres bought in 1903.
HIFRS has praised firefighters and the public for their help in dealing with the incidents.
SRPBA Highlands and Islands regional manager, Drew McFarlane-Slack, said private landowners and their employees had played their part.
He said: "Many of our members have made a huge effort over the last week investing significant time and resources supporting and working with the fire and rescue service and their neighbouring landowners like the National Trust for Scotland and the RSPB to fight the fires.
"This is despite the majority of affected land falling outwith our members' own estates."

McCann's men beat the Highland League champions 2-0 at Dens Park but the manager was less than impressed by the performance.
"The attitude just wasn't there and it was so unlike what we've been seeing up until now," he said.
"I cancelled their day off because we were so poor overall."
Goals in each half from Faissal El Bakhtaoui and Sofien Moussa secured victory for Dee in the Group C match on Saturday.
But McCann expects much better in the upcoming League Cup matches against Cowdenbeath and Dundee United, with the Dens men starting their Premiership campaign at home to Ross County on 5 August.
"There were only a few with pass marks after that performance," he said. "It's hard to explain where that came from and I don't think it was so much to do with disrespecting the opposition.
"You only get what you deserve in this game and we'll speak about why it was like that on Saturday.
"We can't stroll about like that and think we're going to win a game outright just because we're a Premiership team.
"It doesn't work like that in football and they know that."
French authorities are seeking €356m (£276m) in unpaid taxes from Booking.com, according to documents filed by parent company Priceline.
[NEXT_CONCEPT]
Ten Hampden Park-sized football grounds could be fitted into the 332 acres of land calculated to have been burnt in wild fires in the north since 1 May.
[NEXT_CONCEPT]
Dundee boss Neil McCann cancelled his players' planned day off after their below-par showing in the League Cup against Buckie Thistle.