The idea of simply declaring the season over is gaining ground in some quarters but others remain strongly opposed to the suggestion.
The top-flight and second division have already been suspended for three weeks, with 10 rounds each to play, and many of the leading voices are no longer insisting it should finish "whatever the cost."
"There are more uncertainties today," Lyon president Jean-Michel Aulas, an early advocate of ending the league and basing European qualification on last season's final placings which would put his seventh-placed team in the Champions League, told L'Equipe on Sunday.
He added the chances of "finishing all the matches (are) lower".
His counterpart at Brest, Denis Le Sant told the same paper "the season could not start again".
Amiens president Bernard Joannin, whose side are 19th in the table, agrees.
"Denis Le Saint has a very humane position that places the health of all above everything else. It's a view that's shared by a lot of people in the world of football," Joannin told AFP.
"You have to understand that the only commander is COVID-19. Unfortunately, it sets the agenda."
Others were outraged.
"We hope that the league will finish if it's possible. It really bothers me to see in some people a kind of shame that football wants to come back to life at some point," Pierre Wantiez, general manager of Ligue 2 Le Havre, told AFP.
"It's shameful for me to see some people feel ashamed that football wants to come back to life at some point.
"I'm not going to hide behind a veil of secrecy and say, 'It's over, we can't do anything.' Let's wait before saying the season is dead."
'It's urgent to wait'
The situation is confusing leader's across the game.
The lockdown in France has been extended at least until 15 April.
Most clubs have put staff, including players, on part-time contracts and some of the league's foreign stars, including Brazil's Neymar, have gone home.
Broadcasters Canal+ and beIN Sports have suspended the payment of TV rights, the clubs' main source of revenue.
In this context, the French league is increasing the frequency of its conference calls but delaying its decisions.
"Today, who can say what's going to happen? We're preparing for everything. For the time being, I think it's urgent to wait," Olivier Delcourt, president of Ligue 1 Dijon who are three points above the relegaton play-off spot, told AFP.
Amiens' Joannin said he would like the league to follow the government's lead.
"There's no point in talking and saying nothing," said Joannin.
"Let's take the time... We need to give ourselves a fortnight to see how things are going."
The issue of TV rights, will be addressed this week by a quartet of presidents, led by Paris Saint-Germain chief Nasser Al-Khelaifi, who is also head of beIN Media and several sources confirmed negotiations with Canal+ are planned.
The timetable depends on the decision of the French government on when to end the lockdown and to a lesser degree, those of the governing bodies of world and European football, FIFA and UEFA.
FIFA has to change the way the summer transfer market works, because players whose contracts end this season will become free agents in June. UEFA has shown itself open to postponing its Champions League until the end of July or August to allow the domestic leagues to end but has also threatened to bar clubs from leagues that do not finish.
Some officials argue a "deadline" for the resumption of the league must be set quickly.
"A resumption of the season until doomsday should not push the problem onto the next championship," Wantiez warned.