The French daily said talks were still in the early stages, but the trade court in the southern port city of Marseille had been informed.
The third-biggest transporter of containers in the world has been struggling with the restructuring after being hit hard by the global economic slowdown that has slashed demand for goods and transportation.
As part of its plan to recover from the downturn, CMA CGM had been discussing opening up to outside capital, including holding talks with a unit of Qatar's sovereign fund, CMA CGM Chief Executive Philippe Soulie told Reuters in May.
Soule said total investment would be about $500 million.
In an unsourced report, the Le Figaro said Frere had teamed up with an unidentified French investor.
France's strategic investment fund has already agreed to take part in the capital injection.
The paper said the Qatari group was still an option after it submitted an offer at the start of July.
The Saade family currently holds 100 percent of the shipper. (Reuters)
