Fifteen people were stuck in a train station for the night and eight more remained missing in France.
A storm that moved overnight across south-eastern France into north-western Italy caused major flooding on both sides of the border, destroying bridges, blocking roads and isolating communities.
In Italy, a firefighter was killed during a rescue operation in the mountainous northern region of Val d’Aosta.
A search team found a body in the Piedmont region’s Vercelli province, where a man had been swept away by floodwaters late on Friday.
The Italian firefighters used a helicopter to ferry 17 people to safety from the French town of Vievola, including a woman with two grandchildren.
A bulldozer fetched another eight people who managed to climb the Col de Tende, a high mountain pass linking France and Italy, to a tunnel.
Fifteen more people were taking shelter in the Vievola train station after the operation to rescue them was put off until daylight.
The spokesman for Italy’s firefighters, Luca Cari, said a search was ongoing for a missing shepherd who was pulled into floodwaters on Col de Tende.
His brother managed to grab on to a tree and was saved, while authorities were searching on the French side for the shepherd.
The situation at the tunnel on the high mountain pass was complicated by the fact that French emergency responders cannot access their side due to flood damage, Mr Cari said.
Unrelenting rainfall overnight hit levels not seen since 1958 in northern Italy’s Piedmont region, where as much as 630 millimetres (24.8in) of rain fell in a 24-hour period, according to the Italian civil protection agency.
Hundreds of rescue operations were carried out.
— VigiMétéoFrance (@VigiMeteoFrance) October 3, 2020
Eleven campers were saved in Vercelli province, where floodwaters hit 20-year highs.
And Alpine rescue squads have evacuated by foot seven people who were in houses cut off by flooding at Terme di Valdieri; some had to be carried on stretchers due to the muddy conditions and accumulation of detritus.
On the other side of the border, in south-eastern France, almost a year’s average rainfall fell in less than 12 hours in the mountainous area surrounding the city of Nice.
Nice mayor Christian Estrosi said more than 100 homes were destroyed or severely damaged in the area.
French prime minister Jean Castex, who flew over the area in an helicopter, confirmed that at least eight people were missing in France, including two firefighters whose vehicle was carried away by water when a road collapsed.
“I cannot hide our grave concern on the definitive toll,” Mr Castex said.
Many worried families had not heard from their relatives due to mobile phone services being cut off in the area.
“As I speak, priority goes to searching for victims, providing supplies and accommodation for the people affected, and restoring communications,” the prime minister said.
Rescue efforts included 871 personnel working on the ground, as well as military helicopters and troops helping with emergency assistance, Mr Castex said.
French President Emmanuel Macron on Saturday expressed gratitude towards rescuers on Twitter.
“Together we will get through this,” he said.
France’s national weather agency, Meteo France, said that up to 500 millimetres of rain (19.7in) were recorded in some areas, the equivalent of almost one year of average rainfall.
Meteo France issued a danger alert on Friday and all schools in the region had been closed. Local authorities urged people to stay at home.
In central Switzerland, flooding along the Reuss River caused the closure of a stretch of the A2 highway – a major transalpine route.
Further east, 13 residents were evacuated from their homes in the town of Diesbach because of flooding.