Really, it's a wonder that Belgium – straddling the geographic divide between the Netherlands and France and the linguistic divide between Flemish and French – has not come to blows over the French oven and the Dutch oven. We believe yours is not a question of semantics or even national pride, though, more a question of usage.
Le Creuset, the wonderful cookware company based in Fresnoy le Grand, France, (and started by two Belgians), does not make Dutch ovens. It only makes French ovens. Le Creuset's first cocotte was cast in 1925. According to several French dictionaries and online translators, the correct word for cocotte in English is stewpot or casserole. How likely is it that two Belgians, establishing their company at the hub of major transportation lines in France, would name their leading product a DUTCH oven? Not very likely, we think.
Now, Emile Henry, another inspiring French cookware company, also does not sell Dutch ovens – it sells "round ovens" and "oval ovens" and "round stewpots" and "oval stewpots" (OK, its U.S. Web site mentions "Dutch Ovens/Stewpots" in passing, but its other English-language sites refer only to stewpots of one shape or another, which leads us to think that the British and Australians also do not refer to Dutch ovens).
The Dutch, for their part, are probably wondering what in blazes we're talking about. We have no idea what the Dutch call a Dutch oven, but just as the French do not refer to French toast, we doubt the Dutch cook in Dutch ovens. It seems most likely that the name Dutch oven was coined on this side of the Atlantic and had to do with the Pennsylvania Dutch (who, most likely, were German (deutsch) immigrants), rather than the Dutch Dutch.
Clearly, there is no inherent difference between a Dutch oven, a French oven, a stewpot, a round (or oval) oven, or a covered casserole, as long as each has relatively tall sides and a tight-fitting lid, and can be used on the top of the stove or in the oven. They are most often made of cast iron (very often enamel-covered), but some (Emile Henry's) are flame-proof stoneware, and others are stainless steel. The enameled versions can be absolute works of art.
There may be companies out there that use one or more of these terms to describe pieces of cookware that do not fit our tidy definition, and all we can say is shame on them for cluttering an already confused cookware category.