The gold is the second of Hoy's Olympic career after he won the 1km time trial four years ago.
"To win as part of a team is a totally different feeling from the 1km time trial in Athens," said Hoy.
"Our friendship has been so dominant in the last few years. As part of a team, you can't let anyone down.
"To beat them by half a second made it that exciting. Honestly, it took every inch of effort in beating the French who have been invincible.
"The French have been so dominant. We have really put all the pieces of the jigsaw together. We really focused on the details. To stick half a second into them, it's amazing."
Scot Hoy, hoping to win three golds in Beijing, is also competing in the keirin and the men's sprint.
Video - Golden delight for GB spint trio
He told BBC Sport: "There's still plenty in the tank. At the end of the week, if I get three, I'll do a dance for you and that's a promise."
Staff was a member of the team that finished fifth in the event in Athens.
"It hasn't sunk in yet, it's weird, but mostly exciting," he said.
"We were very disappointed after Athens. I've given absolutely everything I could into it and it paid off.
"We've got a fantastically strong team, we showed everyone at the worlds how strong we are."
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