Quinta Industries, a leading French post-production company, was placed in liquidation proceedings on Friday.
Footage of the threatened 36 films is held in computers by the company, which risk being frozen or even wiped clean if creditors are given access to the company's assets.
The federation representing the French film industry sounded the alert in a letter to French president Nicolas Sarkozy warning of "irreversible economic and cultural consequences" of the company's failure.
The 36 films already have planned release dates in France and abroad, meaning that a race against the clock is now underway to get hold of key elements to finish off post-production.
Other films involved include the follow-up film from Jean Dujardin, who was recently nominated for a Golden Globe for his starring role in silent movie The Artist.
Radio station Europe 1 reported on Tuesday morning that an American production company, Film Funds, was planning to make an offer to legal authorities to take over the completion of around 32 films currently in post-production.
"We have the means to do it and we would like to be able to propose to film producers an outcome so these films can meet their release dates," said Christian Paris, one of the vice-presidents of the company.
Film Funds is also offering to take on some of the company's employees.