Speaking at a press conference in Marcoussis on his return from Argentina, where he had to deal with the arrest and subsequent indictment for aggravated rape of two players as well as the expulsion from the tour of another player for posting a racist video online, Grill said players needed "to have a sense of responsibility".
He also conjectured that the two players left behind under arrest in Argentina, Hugo Auradou, 20, and Oscar Jegou, 21, would likely face trial within "nine to 14 months".
The two men were arrested on July 8 in Buenos Aires after a 39-year-old woman accused them of raping her multiple times and beating her in a Mendoza hotel room after the first Test match between Argentina and France, in which they both made their international debuts.
They deny the accusation, saying they had consensual sexual relations with the woman.
If found guilty, the players face between eight and 20 years in prison.
The examination of their request for house arrest is expected to take "at least 10 days", according to the public prosecutor's office in Mendoza.
Grill said Auradou and Jegou had failed to respect the framework governing foreign tours and deflected any blame from the tour management.
"There is an extremely precise (tour) framework which has existed for years, based on autonomy and accountability," said Grill.
"This framework was not respected by the players. It's not the staff who are to blame, it's the players who decided to step out of line."
On the same night, full-back Melvyn Jaminet, 25, made racist remarks in a video posted on social networks, leading to his immediate exclusion from the squad.
'Raising awareness'
A report was made to the public prosecutor on July 12, Grill said on Tuesday, adding that the FFR would be looking to clamp down much harder on anti-social behaviour.
"We're going to step up raising awareness," he said.
"And we're also going to increase the penalties, which will now be financial but could go as far as temporary or permanent exclusion from the French teams.
"For the rest, there will be zero tolerance.
"There will be a before and after Mendoza."
Grill, however, kicked back at suggestions that rugby's traditional 'third half' in the bar afterwards was detrimental in itself with critics now claiming that cocaine is as much in evidence as beer.
At the start of last season, La Rochelle flanker Jegou was handed a one-month suspension when he tested positive for cocaine.
"I don't believe that the spirit of the 'third half' should be called into question," he said.
"On the other hand, the spirit of responsibility, the acceptance of sanctions, the sense of duty, the sense of the collective interest, are also part of the values of rugby.
"And I think we have to be capable of both letting off steam... and at the same time accepting a principle of responsibility and sanctions."
French rugby has had to deal with a number of incidents over the past year with international props Mohamed Haouas and Wilfried Hounkpatin both convicted for domestic violence while lock Bastien Chalureau was also found guilty of assaulting two former rugby players.
