A taskforce of representatives from both houses of the French parliament, the Senate and the National Assembly, said they had agreed on the final elements of a bill now likely to be approved more broadly by other parliamentarians over the summer.
Under the bill, telecoms operators would have to seek formal permission from the French Prime Minister for their 5G network projects, and will need to get clearance based on defence and national security parametres.
French government officials - including President Emmanuel Macron - have said in recent months that their plan to introduce checks and balances was not aimed at blocking Huawei or targeting any equipment makers or operators in particular.
The draft French law does not mention any supplier. But Chinese telecom equipment makers such as Huawei Technologies are in the spotlight over concerns their gear could be used by Beijing for spying - something Huawei denies.
U.S. President Donald Trump's administration moved to blacklist Huawei in May, and Washington is piling pressure on European countries to follow suit.
This come as telecoms operators worldwide are gearing up for the arrival of 5G, which promises ultra-fast mobile internet for those able to make the heavy investment needed in networks and equipment.
The text agreed on by French parliamentarians on Wednesday excludes 4G networks from the planned approval and control process.
(Reporting by Sarah White and Caroline Paillez; Editing by Hugh Lawson)