Reports in France say a bus was in collision with the couple's car in the early hours of Friday.
Collins, 34, made his debut for New Zealand in 2001 and won 48 caps. The ex-Ospreys flanker had been playing for French side Narbonne.
The All Blacks said on Twitter they are "shocked and saddened" by the news.
The tough-tackling blind-side flanker was described as the "Jonah Lomu of the forwards" by World Cup-winning England scrum-half Matt Dawson.
Former New Zealand wing Lomu is one of the sport's greats and in his condolences called Collins "brother".
Ex-All Blacks captain Sean Fitzpatrick said Collins "epitomised everything an All Black should be".
"We say in the All Blacks, a good man makes a great All Black and he was a very, very good man," added Fitzpatrick.
"He was as tough as old boots on the field, very uncompromising and not someone you wanted to play against.
"But off the field he was the nicest guy you could meet. A loving man and very caring."
Wales and Ospreys scrum-half Rhys Webb said it was "devastating news" to hear of the death of "a true rugby legend".
Rodney So'oialo, who played at number eight alongside Collins for the All Blacks, tweeted: "Very sad day to hear a team-mate, and our very good friend Jerry Collins has passed."
England's 2003 World Cup-winning winger Ben Cohen tweeted: "So so sad. Can't believe that Jerry Collins and partner Alana died in car crash in France - RIP."
Collins started his career at Wellington in the National Provincial Championship and also played for the city's Super Rugby outfit Hurricanes.
Renowned for his bleach-blonde hair and ferocious tackling, he made his All Blacks debut against Argentina in Christchurch in 2001.
He also captained them three times and played for New Zealand at the 2003 and 2007 World Cups.
His last match for the All Blacks was the 2007 World Cup quarter-final loss to France in Cardiff.
Later that year, Collins famously turned out for Barnstaple's second XV against Newton Abbot while on holiday in Devon, and wore the team's socks when he played for Barbarians in a win over South Africa in December 2007.
Barnstaple said he "will forever have a special place in our club's history".
He announced his international retirement in 2008 and went on to join French Top 14 side Toulon before moving to Wales to play for Ospreys in 2009.
In his first season with Ospreys, he helped them to a third league title and was voted players' player of the year.
"He was his own man, a true individual and a giant of the world game. Jerry made a huge impact during his short time in an Ospreys jersey and will be sadly missed by everybody in rugby, his family and friends," the Welsh region said.
Narbonne finished one place above the relegation zone in France's second division last season, having been in the relegation places at the start of February.
Collins' former Super Rugby side Hurricanes played against the Highlanders in Napier on Friday and held a minute's silence before their game.
-BBC