Australian Jones has led the team to four successive Six Nations victories, clinching the northern hemisphere's premier international competition with a match to spare.
Vunipola, back to his rampaging best form, said the players were much more friendly than they were during Stuart Lancaster's reign as coach.
"James Haskell never used to talk to me but now we've started talking about stuff other than rugby," Vunipola told the BBC, referring to his experienced back-row colleague.
"After a few games this year he was asking me questions and now we've made a good bond."
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Vunipola described the atmosphere around the squad as "easy-going".
"You can see that new players are coming in and just doing their thing," the 23-year-old said.
"We realised it was something we could improve on, you build stronger and better relationships that way," he added.
Vunipola praised the contribution of Jones and his coaches Paul Gustard and Steve Borthwick.
"He (Jones) has come in and had a good influence on the boys. Not just him, but also 'Guzzy' (Gustard) and Steve Borthwick," he added.
"They know me quite well from Saracens so it's about paying that trust back."
England are bidding to complete the Six Nations grand slam for the first time since 2003 by beating France in Paris on Saturday.
(Reporting by Ed Osmond, editing by Pritha Sarkar)
