The Cap-Rouge, Que., rider will be a support racer on the Europcar team in the 100th Tour de France that begins Saturday on the Mediterranean island of Corsica.
"It's fairly calm now," Veilleux said Friday on a conference call. "Right now, I'm not feeling too much stress and that's perfect.
"I want to be as rested and mentally ready as possible going into the next three weeks."
Veilleux is one of three Canadians entered in the annual trek around France that is considered the world's most prestigious cycling race.
Ryder Hesjedal of Victoria, the 2012 Giro d'Italia winner, is with Garmin Sharp while 36-year-old Svein Tuft, a time trial ace from Langley, B.C., will ride for the Orica GreenEdge squad.
Veilleux said he will only feel the real Tour atmosphere once he is on the bike, in among the spectators who crowd the route.
The event begins with three stages in Corsia, where the crowds may not be as large as they will be when they reach the mainland for the fourth stage in Nice. It ends July 19 on the Champs-Elysee boulevard in Paris.
For now, the 25-year-old is soaking up as much information as he can from his teammates.
"For a team like ours, the Tour de France is the race of the year, so we talk about it all the time," he said.
One thing he learned is that between the racing and the commitments to fans and media, getting proper rest is primordial.
Veilleux is working to establish himself at the top level of bicycle racing. He won a stage of the Criterium du Dauphine this year and then got the honour of being selected for the Tour de France team.
He will be a support rider for Eurocar, working more for Pierre Rolland than for the team's other leader, Thomas Voeckler. Rolland's aim is to finish high in the overall standings, while Voeckler works on his own to try to win key stages.
Voeckler won the polka dot jersey last year as the Tour's top climber.
"Thomas doesn't need five guys around him all the time," said Veilleux. "He's not really looking at the overall standings, so he doesn't need us as much.
"We'll spend most of our time with Pierre, who is looking at the overall standings and can't afford to lose any time. Thomas will still need our help on the big stages to get attacks started or to stay with him on a breakaway."
Veileux's own ambitions are modest.
"I have no expectations as far as results go," he said. "I'll see how the race goes.
"My goal is to do a good job as a teammate, and I really hope to make it all the way to the Champs-Elysees."
But if the chance arises one day to take off on his own, he will likely have the green light to go.
"I'm there to help Pierre and Thomas, but (Europcar management) won't keep me chained to Pierre, as long as it won't hurt him in the overall standings."