The Belgian who is the world’s number seven has been high on self-confidence since he finished runner-up at the ATP Finals last weekend. Goffin played the key points better at the end of the first set and then never looked back.
Although the majority of the 28,500 crowd at the Pierre Mauroy stadium were French, the Belgium fans were the most vocal.
Lucas Pouille had won his previous three encounters with Goffin, all played last year, but Goffin was the more confident and composed player.
The Frenchman whipped several forehand winners but was kept in check by Goffin as both players held comfortably.
Pouille was two points from the set at 5-4, 30-30, but Goffin served two consecutive aces.
The Belgian had the first break point in the following game, converting it when Pouille's sliced backhand went into the net. Goffin then won his service game to love, clinching the set with a service winner.
Our compatriot took an early break in the second when the Frenchman double faulted and he bagged the second set as Pouille made yet another unforced error.
Another early break put Goffin in the driving seat in the third set and the Belgian raced to victory on his first match point.
This weekend's Davis Cup action
On Friday evening French number one Jo-Wilfried Tsonga takes on Steve Darcis in the second first day singles match.
Saturday sees the potentially decisive doubles match featuring France's Richard Gasquet and Pierre-Hugues Herbert against Ruben Bemelmans and Joris De Loore.
The nine-time champions France have not won the Davis Cup since 2001, losing three finals since then, while Belgium, runners-up in 2015, have never yet claimed the title.