Bidding to become the seventh man in the Open era to win back-to-back Roland Garros and Wimbledon titles, Zverev dispatched his opponent in impressive style on Court One.
Zverev was pushed hard by Belgian youngster Alexander Blockx in his opening match, but Royer was no match for the imperious German.
The 29-year-old ended his long wait for a maiden Grand Slam title at the French Open last month but has never performed well at Wimbledon.
He has a golden opportunity to at least reach the quarter-finals for the first time at the 10th time of asking, with Jannik Sinner and Novak Djokovic in the other half of the draw, and fourth seed Ben Shelton already knocked out.
"If I keep playing like this I definitely think it can happen this year," said Zverev.
"In tennis you need to have a short-term memory, whether it's good or bad.
"I won the French Open which for me, I've been waiting for that Grand Slam for such a long time... Two weeks later we're here at Wimbledon and it's such a short turnaround."
After losing the opening game of the first set, Zverev reeled off a blistering run of nine successive games.
Zverev was in complete command as he secured his 50th Tour-level match win on grass.
The second seed, who has appeared in four Grand Slam finals, will face American world number 92 Marcos Giron in the last 32.
Wimbledon 2026
Wimbledon is taking place from June 29th to July 12th at the All England Club in south-west London. With 128 players in the draw, it is the third of the four Grand Slams of the tennis season and the only one played on grass.
Men's singles draw and results | Women's singles draw and results | All you need to know about the tournament | Find all our Wimbledon coverage here