PARIS—Lance Armstrong believes he can win an eighth Tour de France title, well aware his aging legs are not as strong as they used to be. He is also willing to put such ambitions aside if it means helping teammate Alberto Contador win.

Contador, the 2007 winner, and Armstrong will ride for the Astana team in the three-week race that starts Saturday with a time trial in Monaco. The pairing raises an intriguing question: Can the two Tour de France champions ride together or will their fierce individual agendas divide them?

The 37-year-old Armstrong won the last of his rec...

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