Gaston is trying to pressure Belle into marrying him, so naturally he will exaggerate in order to try to make her believe that she will be lost without a husband. Of course, he is not telling the whole truth. While a single woman in France during that period would have been at a disadvantage and excluded from most occupations, it was by no means impossible for them to make a living, or even, in some cases, attain some measure of success. That is not to say that it would have been easy. In addition, Belle grew up pampered by her father and reading books about abstract topics, which would hardly have been conducive to the sorts of trades that a woman could plausibly pursue in a rural town in 1700s France.
Assuming that Clothilde's name, like that of her husband Cogsworth, is meaningful, she may be a washerwoman or seamstress, in the terminology of the period. The former trade was well-recognized, and by the 19th century, there was even a small festival in Paris dedicated to the women who did laundry work.
In addition, Cogsworth had been the majordomo of the castle, a position of some importance. We can presume that he had a decent income and some savings, which may have cushioned any financial difficulties that Clothilde may or may not have had.