Is there a name for this type of heel?

This was the ordinary form for high heels from the end of the 16th to the end of the 19th century (except during the Revolutionary/Romantic era, when heeled shoes went out of fashion); at the time they were simply called "high heels" or occasionally (by those who disparaged their use as effete and foreign) "French heels".

This basic shape, with a recurve profile and flared base, was challenged starting about the 1890s by shapes with single curves and straight profile, narrowest at the base. This shape then came to be referred to as a "French" or "Louis" or "Louis XV" heel (with no disparagement intended), contrasted with "military" heels (straight-sided at both back and breast), "Cuban" heels (straight at the breast, with a tapering curved back, like cowboy boots today), and "spike" heels (tapering at both back and breast to a very narrow base). The French heel finally disappeared in the early 1920s, in part because it was far more expensive to mass-produce.