The Sharks had risked losing the NSW forward for four games by challenging the charge at the judiciary.
But after viewing video footage of the incident and consulting their legal team on Tuesday morning, the club has announced its decision to take the early plea.
Gallen re-opened a nasty wound on the heavily bandaged head of Laffranchi during the incident from Saturday's game at Skilled Park, forcing the Titans forward from the field.
Two of the five players charged from the weekend games were yet to enter their pleas.
But the judiciary will definitely sit on Wednesday night with St George Illawarra forward Jarrod Saffy's contrary conduct charge for allegedly biting Canberra halfback Todd Carney referred straight to a hearing.
Brisbane winger Reece Robinson has also pleaded guilty to a dangerous throw, but will not be suspended.
Melbourne veteran Matt Geyer (contrary conduct, unnecessary face contact) and North Queensland five-eighth Travis Burns (dangerous throw) have until midday to enter their plea.
Geyer will escape a ban by pleading guilty, while Burns is facing a one-match suspension.
Gallen will now be available for the round seven match against Wests Tigers, with the backrower to miss games against St George Illawarra, South Sydney and Penrith.
The suspension comes just a week after prop Ben Ross was rubbed out for seven games for striking Manly half Matt Orford, and with the Sharks already missing four others, including in-form forward Reece Williams and Brett Seymour (both knee), to injury.
Despite branding the incident as "stupid", Sharks coach Ricky Stuart on Tuesday said he had never considered stripping the captaincy away from the inspirational forward.
"Certainly, I wouldn't take the captaincy off Paul for this, no," Stuart told Sydney radio 2KY.
"I've got a bloke that is very passionate and emotional about the job and there's no way that I would take it off him.
"It's just something he has to learn from.
"I'm disappointed, but disappointed for the players. We got off to a good start and now we've got six players sitting on the sideline and two players are there because of their own stupid actions."