As for tax-efficient ways, my french isn't that good so I don't know the details but if I understand this topic  correctly you should have some options like PEA, PERCO/PERP, and/or PEE/PEI/PEG
N.B.: There will always be some discussion around this specific broker because their 'default account' contains a clause where this broker is allowed to temporarily loan your assets to other customers. Don't do this. You can get a so-called 'custody account' (which is basically a regular brokerage account) that's only marginally more expensive.
Open an ETRADE Securities account if I'm neither a legal resident of the U.S. nor a U.S. citizen
You won't be able to open a brokerage account online if you are not a legal resident or citizen of the United States because we will need some additional documentation from you. If you're not sure if you're a legal resident, see the Help topic Determine my residency status.
Request a brokerage account application by mail, or download it from our Forms & Applications page.
Download a Form W-8BEN.
Complete sections 1 through 6 of the application (the section on options trading isn't required).
Send your completed application and Form W-8BEN, along with your initial deposit and any supporting documentation, to us at:
By regular U.S. mail
ETRADE Securities LLC
PO Box 484
Jersey City, NJ 07303 - 0484
By overnight mail
E*TRADE Securities LLC
Harborside Financial Center
501 Plaza 2
34 Exchange Place
Jersey City, NJ 07311
As per how to open a brokerage account for alien non US resident, several years ago I managed to open an account at interactive broker while living in hong kong. They have among the lowest fees of all brokers and good software. Pretty sure its also possible to open an account while residing in france.
One thing to note though: as an alien non US resident, any US dividends will be taxed at 30pct in the US, directly deducted by the brokerage company
Why? Surely investing in a higher growth economy is better?