The 25-year-old was at the heart of Didier Deschamps' triumphant side in Russian Federation but returned to a hard situation at United after being dropped from Jose Mourinho's starting XI towards the end of last season.
Jose Mourinho last month stripped Pogba of the United vice-captaincy amid reports of frosty relations between the two during the Red Devils' hard start to the 2018-19 season.
Hugo Lloris lifted the trophy in Moscow in mid-July as Didier Deschamps' captain, and Pogba said he would continue being an influential figure in the squad even if he never replaced the Tottenham goalkeeper.
"I've never played in the France team to be captain, being here is already a big thing for me", he said, according to the Daily Mirror. "You don't have to be captain to speak". As a leader you can talk on the pitch, but I have seen leaders who do not necessarily speak.
He cited former Italy midfielder Andrea Pirlo, a teammate of Pogba's at Juventus, as someone who could be relied upon to "show you the way on the pitch".
"The armband has never been a goal".
Manchester United's Paul Pogba has said he has struggled to focus following France's World Cup win - but has insisted he can still lead the club despite being dropped from vice-captaincy duties.
"Because otherwise you can have this image, 'Ah, he does not want to talk because he's upset, ' when you are not at all".
The LA Galaxy striker further added: "But a coach is only as good as his team, so it's not like he can do miracles if the team is not good enough".
"I'm not going to get into it, whether it's (Antoine) Griezmann, Kylian (Mbappe) or Raphael who deserve it much more than me".
Mourinho said at the time: 'The only truth is that I made the decision of Paul not to be the second captain any more but no fall-out, no problems at all.
'I want to be a mark in the history of football.