European trade ministers will Friday try to salvage the mooted accord, just days after large-scale public protests, notably in Germany.
French Trade Minister Matthias Fekl has also urged the EU to walk away from negotiations on the planned pact.
The Transatlantic Trade and Investment Partnership (TTIP) would create the world's biggest market of 850 million consumers, stretching from Hawaii to Lithuania -- if politicians can drag it over the line.
French businessmen say they hope the effort will succeed.
"French firms call for negotiations between the European Union and the United States to be pursued, without naivety," said a joint statement from France's largest employers' federation Medef, the GFI industrial federations' group and textiles association, UIT.
"Simply to abandon this historic trans-Atlantic project after just three years of discussions would seem to us to be a most serious act," it said.
The group warned that "to put oneself outside the alliances created would weaken our firms' capacity to export and be competitive in a globalised (market)."
While calling on Paris to maintain a dialogue on the thorny issue with fellow European negotiators, the French groups recognised that some US proposals on the table were "not acceptable".
There are, for example, fears on the European side that an accord could undercut the 28-nation bloc's standards in key areas including health and welfare.
Fekl was expected to demand at Friday's meeting of EU counterparts in Bratislava to pull the plug on the proposed deal, while Brussels has said the European Commission is pursuing discussions in Washington.
The deal, under negotiation since 2013, has become a hot potato as elections approach in the United States, France and Germany, despite hopes it could break down trade barriers to give a fillip to a doggedly sluggish economic climate.