All six British singles players lost in the first round last year and Dan Evans and Heather Watson were both beaten in their opening matches here.
But Norrie, who has been in brilliant form on the clay this year, avoided joining them with a 7-5, 7-6 (5), 6-2 victory over American qualifier Fratangelo.
The British number two has reached ATP Tour finals in Estoril and Lyon over the past month and beaten two-time French Open finalist Dominic Thiem, so expectations were high for his campaign at Roland Garros.
He struggled to find his best form over the first two sets in breezy conditions but showed what makes him such a gritty competitor as he withstood consistent pressure on his serve in the opener before seizing on a dip by his opponent.
Norrie, who could meet Rafael Nadal in the third round, was pegged back from 4-1 in the second but came through it on a tie-break and loosened up in the third set to reach the second round at Roland Garros for the second time.
There the world number 45 will take on either 26th-seeded Italian Lorenzo Sonego or Lloyd Harris of South Africa.
Watson’s poor run continued with a first-round defeat by Zarina Diyas. The 29-year-old had won just one of her last seven matches prior to arriving in Paris, with that sole victory coming against a player ranked outside the top 400 in the Billie Jean King Cup last month.
She cited niggling injuries as a contributing factor and had her right shoulder strapped during a 6-4, 7-5 loss to 93rd-ranked Kazakh Diyas.
Watson could not have made a better start, breaking the Diyas serve in the first game, but from 4-2 the British player fell to pieces, spraying the ball wildly and losing four games in a row.
Across the end of the first set and beginning of the second, Watson lost 15 points in a row, before she regrouped to hold serve for 1-1.
She began to play better again and, in a repeat of the first set, moved into a 4-2 lead only for Diyas to level once more.
Watson managed to hold serve at 4-5 this time but came unstuck in her following service game, dumping a simple volley into the net on match point to suffer a second successive first-round loss at Roland Garros.
Evans, meanwhile, suffered a first-round loss to Miomir Kecmanovic on Sunday.
It was the British number one’s fourth time in the main draw at Roland Garros and he is yet to make it through to round two, going down 1-6, 6-3, 6-3, 6-4 on this occasion to 21-year-old Serbian Kecmanovic.
Clay has always been Evans’ weakest surface but expectations both internally and externally had been raised by his success on it this season, including a stunning victory over Novak Djokovic on his way to the semi-finals of the Monte-Carlo Masters.