The 37-year-old former Real Madrid midfielder made a surprise move to the big-spending Ligue 1 club on transfer deadline day last month when many had written him off.
The transfer grabbed the attention of the world's media but after signing a five-month contract and agreeing to donate his salary to a children's charity in Paris, Beckham now has to prove he can still contribute on the pitch.
Former team-mates Giggs and Scholes are still playing at United in their late 30s, albeit on a bit-part basis, and their roles are a template for Beckham.
"I might be able to create good things that happen off the field but on the field is where I want to be successful. I want to be a champion and I want to win trophies," he said in an interview with Al Jazeera and talkSPORT radio.
"That's been my mentality all the way through my career. Your motivation never changes, once you have that motivation in you it continues throughout your whole life.
"Players like Ryan Giggs and Paul Scholes at Manchester United, they don't play every game but when they do play they are big influences in the game. So I am looking to do that to continue to be successful."
Beckham has not played competitively since he left Los Angeles Galaxy at the end of the Major League Soccer season in December.
He spent a few days training with Premier League side Arsenal but expects it will take time before he is ready to make his Ligue 1 bow.
"I feel pretty good, it will take me a couple of weeks at least to get up to speed with the rest of the team but I think I have always kept myself pretty fit," said Beckham.
"I have taken time off and trained with Arsenal for a couple of days and once I get in with the team I don't think it will take me long to get up to speed. But I want to get playing as soon as possible."
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