Do French Shallots Set Seed

Are French shallots ever raised from seed or are they only able to be produced vegetatively? Which shallots deserve the title of the true shallot? How do the seed shallots that are available from various sources compare with the ones that are usually vegetatively propagated shallots?

The four varieties we offer ave well defined flavours with the garlic flavour being strongest in the French shallot and being absent from the Dutch shallot. The gray shallot has a mild garlic flavour and a strong onion lavour. Many experts consider it to be the true French shallot. What we call the French shallot has a strong garlic flavour and a mild onion flavour. I have never had the garlicky shallots produce any flowers and hence no seed. But undoubtedly some strains exist that flower more freely, but this would be at the expense of bulb formation.
We used to carry shallot seeds (they were hybrid) until they were discontinued by the supplier. They were called French shallots but they looked more like Dutch. They did, however, flower readily, which I think turned out to be a big drawback. The variety was pretty uniform, however.
I think it is fair to say that the vegetativly propagated varieties are higher yielding and have better, stronger taste, and could be hardier. The advantage of the seed grown ones are that they are cheaper to plant and they don't have problems with disease transmission from generation to generation. Also, they don't require that farmers hold back a part of their crop to plant the next crop – they can sell all of their harvest.