His next opponent will be Lleyton Hewitt, who won Wimbledon in 2002 - the year before the Swiss star began his run of five straight titles.
Federer surprisingly dropped serve in the opening game. But he immediately broke back and was in control the rest of the way as he sailed to victory in 1 hour, 21 minutes. The rain delay before the match lasted longer - 1 hour, 41 minutes - the first rain of the tournament.
"Again, difficult conditions, tricky opponent," Federer said. "The wind was swirling. I got down a break in the first game and had to rally back. I played really well throughout the match considering the circumstances."
Federer hasn't dropped a set so far in the tournament. "It's always nice," he said. "Couple of days off now. Hope I play as well next week. It's important to try to keep the game where it is."
Hewitt, who has been troubled by a chronic hip injury and is seeded No. 20, served 14 aces and beat Italy's Simone Bolelli 6-1, 6-3, 7-6 (2).
Federer leads Hewitt 13-7 in career meetings and has won 11 straight going back to the Australian Open in 2004. They have played twice before at Wimbledon, with Federer winning in the quarterfinals in 2004 and semifinals in 2005.
"The next round will be much more difficult," Federer said. "We've played maybe over 16 times. He's a former No. 1 and Grand Slam champion. Should be a great match."
The 31-year-old Gicquel, who had never gone beyond the first round at Wimbledon, has a big serve and strong forehand but couldn't trouble Federer. Gicquel saved a set point on his own serve at 3-5, but Federer closed it out in the next game with a 129 mph ace.
On the final point of the second set, Federer whipped a forehand that left Gicquel lunging and doing the splits. Federer cruised through the third set in 20 minutes.
In women's play, advancing in early third-round matches were No. 4 Svetlana Kuznetsova, No. 8 Anna Chakvetadze and No. 18 Nicole Vaidisova.
Two-time women's champion Serena Williams was up against 2006 winner Amelie Maursemo on Centre Court, while top-seeded Ana Ivanovic was paired on Court 1 against China's Zheng Jie.
Two of Federer's main challengers are already out of the tournament. No. 3-ranked Novak Djokovic, the Australian Open champion who had loomed as a possible semifinal opponent, was upset in the second round by Marat Safin. Two-time finalist Andy Roddick was bounced out Thursday by Janko Tipsarevic.
Roddick was in the bottom half of the draw along with No. 2 Rafael Nadal, who has lost to Federer in the last two finals.
Roddick wasn't the only big upset victim Thursday. Earlier in the day, 2004 champion Maria Sharapova was stunned 6-2, 6-4 by 154th-ranked Alla Kudryavtseva, her earliest loss in a Grand Slam tournament since her first full year on the tour in 2003.
