The second-row will now miss the start of the Rugby World Cup in Japan.
He is suspended for France's opening Pool C matches against Argentina, the United States and Tonga. He will be available for the final pool match against England on 12 October.
Gabrillagues was cited for alleged foul play after the game against Scotland at the Allianz Riviera.
In the 16th minute of the match he made contact with Barclay's head, contrary to Law 9.20 – "a player must not charge into a ruck or maul".
World Rugby said its disciplinary committee chaired by Simon Thomas (Wales) alongside Donal Courtney (Ireland) and Valeriu Toma (Romania), viewed footage with various angles of the incident.
Gabrillagues accepted it was foul play worthy of a red card.
A World Rugby statement said: "The committee deemed that it was intentional, the offence took place at considerable pace and with considerable force to the opposition’s head such that the player sustained an injury."
An offence of that gravity carries a minimum 10-week suspension but having noted Gabrillagues’ early admission of guilt, his apology and expression of remorse to his opponent and his good conduct at the hearing, the disciplinary committee reduced the ban by 40 per cent, resulting in a ban of six weeks.
Taking into account Gabrillagues’ playing schedule, the suspension will end at midnight on Sunday, 6 October, 2019 after which he is free to resume playing.
The player has the right to appeal the decision within 48 hours of receiving the written decision.