There are no really tax exempt purely financial investments products available in France, except limited vehicles such as the Livret A
The closest equivalent (If my understanding of the UK ISA after a quick google search is correct) is the "Plan d'épargne en actions", usually called "PEA", which is a investments account with some fiscal incentives and limitations:
- You can buy any eurozone listed company share (with some exceptions), and any eligible mutual fund or ETF (assuming your broker offers them).
- Weirdly, this can includes some non eurozone trackers
- You can invest up to 150 000 € (the value of the account can exceed this limit, but you won't be able to add more cash)
- The capital gains are subject to a flat 17.2%* "Prélèvements sociaux" (Social security contribution ?) "not-a-tax"
- If you wish to withdraw your money before the account 5th anniversary, the gains are subject to an additional 12.5% "Income tax", and you must close your account (with some exceptions)
* As of today. Actual taxation will depend of the rules in place when you will want to retrieve your money
Here the French government page about the PEA, and don't forget to check your provider of choice fees and available securities
Another popular investment product in France are the "Assurance vie" (that means Life insurance but if my understanding of UK/US money things is correct, that's a completely different product). They come in a lot of varieties, understanding what the "UC" means and comparing fees is difficult, but the tax on them are lower (assuming you keep it at least 8 year), and some of them allows you to buy trackers and sometime individual shares.
Or just buy a flat to let, for which the French Government has a long history of giving fiscal incentives.