An excellent solution
I am a non-EU business owner starting a new business in France, but my situation will be similar to any other non-EU country.
To create a company in France, one must deposit an initial amount of shareholder's equity into a bank account, but it is pretty much impossible to open a bank account remotely if you do not have EU residency or identification (even despite the proliferation of online-only neobanks). The articles and guides online, though many, did not actually provide many alternatives and were written from an EU-centric (or UK-centric before Brexit).
I chanced across this French-language-only website when searching for French terms, but it can be easily translated into English.
In short, Mr Attali's law firm provided an ideal solution. I would say it's something like a trust account or escrow account, deposited with (or in the name of) a public association. In any case, it is sufficient to meet the requirements, to get the company registered and the all-important Kbis (official company extract) that is required for most business dealings in France.
As with any new business relationship with someone found over the internet, one must satisfy themselves of its legitimacy. I decided to proceed after checking various public records (all free searches) such as Mr Attali's registration on the bar/lawyer registry, the various companies registries (there are multiple in France) and any other online sources I could find. You must of course also carry out your own due diligence.
You will be required to complete straightforward identity and KYC checks. I was fine with giving that information after having checked its bona fides.
You will need to communicate in French, but translation apps make it feasible. Although the initial and main interface is an online portal, the primary means of communication is via email and WhatsApp, which is easy.
I have found Mr Attali to be responsive, efficient, and easy to communicate with (but it will need to be in French - so I have limited myself to written comms only). He will pick up and suggest commonsense solutions. His fees are transparent and very fair.
Since that initial matter, we have engaged him to act for us on a number of other legal matters, and envisage that we will continue to do so. I would have no hesitation recommending to others.