French human rights campaigners have criticised Tuesday's plea deal given to French cement maker Lafarge but insisted the company's legal problems were far from over.

Lafarge pleaded guilty in a U.S. court to a charge that it made payments to groups designated as terrorists by the United States, including so-called Islamic State, so that the company could keep operating in Syria.

It agreed to a $778 million fine over conspiring to provide material support to U.S.-designated "foreign terrorist organisations.”

Sherpa filed a complaint against Lafarge in France that prompted a criminal investigation into whether the company was complicit in crimes against humanity.

The U.S. deal "does not allow for a public debate and for the victims to be heard, to be able to ask for reparations" said Anna Kiefer, Sherpa's advocacy and litigation director.

Kiefer added: "We must not forget that there are victims in this case (who were) put in danger because…they were forced to stay and had to pass through checkpoints, and some were kidnapped. It is necessary that the justice system shed light on all these elements and that the victims can also obtain reparations."

Lafarge had denied charges that it was complicit in crimes against humanity. The French investigation, which concerns acts partially committed in France, is ongoing, a person close to France's anti-terrorism prosecution office, told Reuters on Tuesday.

Kiefer concurred, saying: "The French procedure, which is independent, continues. The impact will need to be analysed but the offences are different."

She added: "We hope that, once the investigation is finished, it will be sent to trial where Lafarge, as well as the CEOs, will be able to face trial."

Unlike in the United States, the group does not have the option of negotiating a settlement, which is not allowed under French anti-terrorism statutes.

Separately, Lafarge's former CEO Bruno Lafont accused the company's new owners of leading a "biased" inquiry to blame him for terror financing claims in Syria, a day after the landmark US fine.

Lafont, who was chief executive from 2007 to 2015 when the company merged with the Swiss building supplies company Holcim, strongly denied "ever being informed of any payments to the benefit of terrorist groups or any provision of supplies to such groups," according to a statement issued through his lawyers.

The former chief, who has been charged with "financing a terrorist organisation" in the French case, accused Holcim of singling him out for blame.