The incident took place around 6am local time on the boulevard Saint-Germain on the Left Bank, after “a dispute” between two groups said a police source.
The groups separated but the alleged perpetrators “returned shortly after with a vehicle and fired shots,” said the source.
“Several bullet marks” were found on the spot, added a source close to the investigation and the sportsman died on the spot as a result of these injuries.
A murder investigation has been opened, the Paris prosecutor’s office told AFP.
The suspects were still being sought late Saturday morning, according to sources close to the case.
One of Aramburu’s group, a former Biarritz team-mate who wished to remain anonymous, told AFP they were in a well-known bar, the Mabillon ending their night out with hamburgers.
“There was an altercation, as there can be at the end of the evening,” the source said. “It was settled but the men came back and fired at Aramburu who took three bullets.”
Aramburu was 42 years old. He was a back who won 22 Argentina caps and played in the 2007 World Cup in France, scoring a try as the Pumas beat the hosts in the third-place playoff.
He played club rugby in France for Biarritz, Perpignan and Dax (2008-2010).
He won the top 14 twice with Biarritz (BOPB) and later sat on the club’s board of directors.
Since his retirement from sport, he had lived in Biarritz and worked for a tourism company.
“We learn of the death of Federico Martin Aramburu in tragic circumstances. The whole of the BOPB addresses its most sincere condolences to his family, his close relations, and assures them of its total support,” tweeted the club on Saturday morning.