The paper said the Holcim board met early Saturday and that of Lafarge late in the day, but did not give a source.
The two companies had confirmed talks to merge .
"Holcim and Lafarge believe that... there is rationale in considering a potential merger that could deliver significant benefits to customers, employees and shareholders," they said in separate but near-identical statements.
The new group's headquarters will be in Switzerland, with company sites both in France and Switzerland.
Bruno Lafont, CEO of Lafarge, will be in charge of operations as CEO of the new group. Le Figaro said the new president would be Swiss.
The Swiss company had said that talks were at an "advanced" stage.
On its website, Lafarge describes itself as the global number one for cement, number two for aggregates and number four for concrete.
Industry observers note that the berths in the rankings vary according to methodology.
According to a 2013 ranking by specialised trade magazine Global Cement, which assesses overall output capacity based on a broad range of factors, China's Anhui Conch had an annual output capacity of 217 million tonnes, followed by Lafarge with 205 million tonnes and Holcim with 174 million tonnes.
The combined clout of Lafarge and Holcim would therefore create an industry behemoth.
Founded in Switzerland in 1912, Holcim employs 71,000 people, with production sites in around 70 countries and a market presence on every continent.
It notched up net sales of 19.7 billion Swiss francs (€16.1 billion, $22.2 billion) in 2013.
Lafarge began as a French limestone-quarrying company in 1833, and now employs 65,000 people in 64 countries, with sales of €15.8 billion.
After having surged as rumours swirled concerning the merger talks, both companies' shares remained buoyant at the close of trading in Zurich and Paris.
Shares in Holcim soared 6.9 percent to 80.20 francs, while Switzerland's SMI index fell 0.21 percent.
Lafarge's shares jumped 8.9 percent to 64.09 euros, as Paris' main CAC 40 index gained 0.79 percent.