"The reception I got today was crazy. It was really nice to see a full stadium for a first round like this. It was a beauty. So I'm very, very happy," Federer told a news conference.
The Swiss third seed used one hour and 41 minutes to overcome Sonego 6-2, 6-4, 6-4 through 36 winners, setting up a second round encounter with Germany's Oscar Otte.
The 20-year-old Stefanos Tsitsipas, seeded No. 6, lived up to high expectation on him by conquerring Germany's Maximilian Marterer 6-2, 6-2, 7-6 (4).
Seventh-seeded Kei Nishikori and No. 11 seed Marin Cilic also secured men's singles second round berths in straight sets.
But last year's semifinalist Marco Cacchinato found it unable to replicate success 12 months ago as the No. 16 seed lost a gruelling five-set thriller to local favorite Nicolas Mahut 2-6, 6-7 (6), 6-4, 6-2, 6-4 after three hours and 18 minutes.
In her Roland Garros debut, the 81st-ranked Potapova, 18, produced the biggest upset of the opening day action by seeing off three-time Grand Slam winner Kerber 6-4, 6-2.
Potapova won 82% on first serve and led winners 28-16, registering her first career top 10 victory.
The Russian continued her momentum following a 6-4 opening set victory to take four games in a row into the second set.
Kerber cut the deficit to 4-2 afterwards, but failed to come closer and crashed out from the competition with a forehand sailing wide in the eighth game.
She was unable to complete a career Grand Slam at least this year following victories in the 2016 Australian Open and US Open, and 2018 Wimbledon.
Potapova will next face Marketa Vondrousova of the Czech Republic, who knocked China's Wang Yafan out of the competition 6-4, 6-3.
Both players traded breaks early on. Then Vondrousova showed crosscourt skills to lead 4-1 midway through the first set. Wang moved closer to Vondrousova with two games in a row afterwards, but the Czech steadied for a 6-4 win.
Vondrousova had an early break in the second set and went on to build a 4-2 advantage. Although Wang came back from 40-0 down in the seventh game to maintain her serve, Vondrousova managed to secure her second round berth at 6-3 with her fifth break of the match.
No 2 seed Karolina Pliskova and last year's beaten finalist Sloane Stephens also sailed through the first round. The ninth-seeded Elina Svitolina of Ukraine saw off American veteran Venus Williams 6-3, 6-3.
Novak Djokovic and Rafael Nadal highlight Monday's action in the men's singles opening round, while China's Zhang Shuai is scheduled to put on her Roland Garros opener in 2019 against Varvara Lepchenko of the US.