Whitelock played the last of his 153 Tests, an All Black record, in last month's one-point loss to South Africa in the World Cup final.
He failed to become the first player to win the tournament on three times having won the Webb Ellis trophy in 2011 and four years later.
"I don't think any rugby player that goes so close ever gets over it but you learn that you can't change history," Whitelock told reporters during his presentation as a Pau player.
"Hopefully I can take what I experienced and put a good spin on it at some stages," the ex-Crusaders forward added.
As is often the case after a World Cup, a host of All Blacks players have chosen to leave New Zealand for lucrative contracts abroad.
The majority this time around, including captain Sam Cane, World Rugby player of the year Ardie Savea and first-choice half-backs Aaron Smith and Richie Mo'unga, have signed deals in Japan.
From this year's World Cup vintage only 35-year-old Whitelock, winger Leicester Fainga'anuku and prop Nepo Laulala have agreed moves to France and its gruelling 10-month season.
"It's a different way of life coming to France," the bearded Whitelock said, having moved over with his wife and three children.
"We’ve gone from winter to winter, we'll try and sneak away to some warmth at some stage.
"I'm looking forward to experience different things," the former Panasonic Wild Knights lock added. 'Family cheek'
In France, Whitelock will be captained by his sibling and eight-time All Black Luke Whitelock, who turns 33 in January having been at Pau since 2019.
"My little brother Luke has been sowing seeds, dropping hints, for the last three, four years," Sam Whitelock said.
"There's been a bit of cheek in the family, asking if I am going to listen to him if tells me what do?
"We'll have to wait and see if that's true," he jokingly added.
The older Whitelock joins a Pau side flying high in the Top 14 in second place having been involved in the relegation scrap since their most recent promotion in 2016.
Their last French top-flight title came in 1964.
Whitelock is not expected to make his debut until at least December 16's Challenge Cup game with Welsh region the Dragons.
"The club's been doing outstanding so if anything it's increased the pressure," the 2.02m (6.6ft) tall Whitelock said.
"I have to come here and perform.
"I have to add to the momentum that has been started," he added.
