The star CAC 40 index grabbed 0.36 points to 5,955.01 points around 10:05 GMT.
The day before, he had taken 0.40%.
Chinese Vice Premier Liu He held talks with US Treasury Secretary Janet Yellen on Tuesday, Chinese state media reported, as Washington plans to lift customs surcharges on some Chinese goods, stemming from the Trump administration.
The first round of additional tariffs expires on Wednesday.
Investors hope that these measures could revive trade between the two countries, which would alleviate some pressure from inflation in the United States.
To fight against rising prices, the US central bank (Fed) has indeed undertaken to tighten its monetary policy, even if it means causing a slowdown in activity.
The most important events of the week will take place in the coming sessions, with the release of the minutes of the last Fed monetary policy meeting on Wednesday, then employment and production indicators the following days, warns Jeffrey Halley , Oanda analyst.
For investors, "we will have to remain patient" unless they want to take many risks on the course, he believes.
The fear of recession concerns the United States but also the euro zone, much more destabilized by the war in Ukraine.
The price of European natural gas thus tightened further on Monday and continued to rise on Tuesday at the start of the session.
It reached 171.00 euros per megawatt hour for the Dutch TTF, which refers, an increase of 18% in three sessions.
In addition, in terms of indicators, French industrial production stabilized in May, thanks in particular to the rebound in manufacturing industry, after a decline of 0.3% in April, INSEE said on Tuesday.
First chaotic steps for Deezer on the Paris Stock Exchange
The French music streaming platform Deezer plunged 14.14% to 7.30 euros, for its first day of listing on the Paris Stock Exchange.
The French competitor of the Swedish group Spotify was taking its first steps, a few minutes after the bell rang at the premises of the stock exchange operator.
© 2022 AFP