If the SPV used for your investment is a French Civil Company (Société civile, "SC"), you might have heard that you're personally and indefinitely liable for the loss of the company.
This is correct but the context of the investment in the SC and its rules of governance should mitigate this exposure.
In most cases, the SPV in which you invest will itself invest in a limited liability company (the "Target"), such as a French SAS. This means that if the Target suffers losses, the creditors of the Target could not, in principle, turn against its limited partners (such as the SPV) to obtain the payment of their claims. The liability of each limited partner (such as the SPV) will be capped to the amount invested in the Target.
In respect of this investment in the Target, and provided that such Target is indeed a limited liability company, your liability as an investor of a French SC is therefore limited.
Your exposure as a partner of the SC is therefore only triggered if the SPV suffers losses. However, the SPV will carry no commercial operations and the governance rules of the French Civil Company foresees that any decision (other than purely administrative ones) should be taken by the investors themselves. As such, the risk that the SPV would suffer losses that are not covered by its initial capital (i.e., your investment and that of the other investors in the SPV) is rather limited too.
Obviously, as with any investment in private markets, your investment is risky and you might suffer the total or partial loss of the capital that you invested through the SPV.