Under French law an offer accepted is binding. There are financial penalties for the buyer, calculated on the offer price, if they renege on the offer, which is formal and signed or. They are, however, allowed to certify, at the time of signing, that they are arranging finance, in which event there is no penalty if the fance fails and they are obliged to withdraw on that account. There are penalties for the vendor who withdraws, too.
Now, it sounds as though the person has made an offer with that condition attached. The vendor, having accepted that offer, is currently bound by it. Naturally, the immobilier would be happier with your offer , you having no finance required, since it is definite and quick and he gets his commission more quickly.
Common sense dictates that there must be some kind of time limit, or other condition, imposed by law on these offers, otherwise everyone would be making them 'on spec' and with little or no hope of getting finance, and freezing the sales of property all over France. Without checking,but with long experience of having and, necessarily, buying and selling property in France, my guess is that, additionally to any time limit, the offeror is bound to state which lender(s) he has applied to, so as to show genuineness and give something that could be checked.
Lending on property in France is very strictly controlled. The customer and their spouse or partner have to produce clear evidence of income and all expenditures, so as to give a precise figure of net monies in hand, and the multiplier of that is then applied. Any mistake or generosity on the lender's part will count against them if the borrower is unable to keep up payments because of it.