This seems, based on a little Googling, to turn up in both singular and plural forms (Frenchman and Frenchmen), followed by both disease and disorder; I don't know whether the medical literature is more consistent. D.I.: 'As part of the survival instinct, most animals (including humans) react to sudden, unexpected stimuli with a startle reaction... In a normal individual, the muscular reaction subsides within a couple seconds if no real threat is detected, but for a sufferer of the Jumping Frenchman of Maine Disorder, an unexpected stimulus results in a somewhat different experience.
'An individual with this disorder has a genetic mutation that prevents "exciting" signals in the nervous system from being regulated, which causes a number of bizarre irregularities in their startle response. Most notably, an event which might startle a normal person will result in an extended, grossly exaggerated response from a jumper, including crying out, flailing limbs, twitching, and sometimes convulsions. Because a jumper is almost immediately susceptible to another jump soon after an episode ends, there have been reports that sufferers are sometimes teased mercilessly by people who find the reaction amusing, and trigger it repeatedly.'
Edit: Null Hypothesis denies the genetic aspect: 'Originally described by G. M. Beard in 1878, Jumping Frenchman of Maine Disease is an exaggerated "startle" reflex. It was first noted among related French-Canadian lumberjacks in the Moosehead Lake area of Maine. Initially thought to be a neurological and even an inherited disorder, later researches now suspect the disorder to be psychological and brought on by the stressful conditions in the lumber camps.' (That article uses both the singular and the plural forms, incidentally.)