The fruits I've tried have a brown sugar flavor, not too sweet but certainly not tart. They also have a surprisingly firm texture. They're juicy, but not to the point that you have to eat them hovered over the sink.
Their firmness makes french prunes a really nice lunchbox snack. They can handle a little bouncing and won't leave your fingers too sticky.
And, of course, they're a great cooking fruit. Pies, cobblers, even clafoutis: they do marvelously. Try them in this Prune Plum Pie or this Plum Pandowdy. And of course, you can't go wrong cooking these plums down and serving them over ice cream.
Here in California, you can find French plums at the farmers markets. In other parts of the country, look for them at Whole Foods and gourmet markets.
Have you ever tried these little plums?
Related: In Season Now: Italian Prune Plums