Yes, though as you would be working in France your employer must pay French social security contributions.
The situation would be different if you were living in France but commuting to Italy.
EU rules say cross-border workers pay social security contributions to the country where they work.
You could set up a French business and charge the Italian company for your work.
If the company has a branch in France that can employ you, that also is no problem.
However, if you would be directly employed by the firm in Italy, it would need to pay contributions to the Centre National des Firmes Etrangères and abide by French working practices, such as offering you a subsidised health mutuelle.
The firm has to register with the CNFE on form E0 to obtain a Siret number and to open an account to pay the contributions to CMFE. There is more information at tinyurl.com/y66gwohw and tinyurl.com/yybg63gg.
Reader's query answered by Hugh MacDonald
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