Barrère (ATP-242) had received a wild card. Goffin, the world's number 13, didn't waste too much time and took it 6-3, 6-3, 6-4. Goffin is Belgium's biggest hope in Paris.
The 25-year-old is making progress slowly but surely and eyes a place in the top-10. "I am really happy I could finish it off in less than 2 hours", he said. His next opponent will be Argentina's Carlos Berlocq, a 33-year-old veteran who is ranked just outside the top-125.
In the women's tournament, Yanina Wickmayer reached the 3rd round after beating Ekatarina Makarova of Russia in 3 sets: 2-6, 6-2, 6-2. It was a confidence-boosting for the 26-year-old from Antwerp, as Makarova was the 27th seed in Paris. Wickmayer will next meet 22-year-old Garbine Muguruza, the world's number 4.