This Edison Company chase comedy with an overly-long title is a plagiarized remake of the American Mutoscope and Biograph Company's (AM&B) "Personal", which was made and released earlier the same year. In fact, AM&B unsuccessfully sued Edison over it. Such plagiarism was rampant in early cinema; every distributor did it. For foreign films especially, they generally didn't even bother remaking it, but, instead, simply duped the prints and sold them as their own. The most famous example of this is probably the American distribution of Georges Méliès's "Le voyage dans la lune" (A Trip to the Moon) (1902). American film innovators like Edwin S. Porter, the filmmaker of this remake, essentially learned film technique and were encouraged to produce more-complicated story films through the process of duping and remaking the then more-advanced films of Europeans like Méliès and G.A. Smith.
According to Charles Musser (using both his "Before the Nickelodeon" and "The Emergence of Cinema" as sources), the Edison remake probably sold better than the original "Personal". The remake undermined AM&B's distribution practice of initially exhibiting their films to licensed theatres on the vaudeville market while withholding the pictures up to several months before selling them to everyone else. This system allowed Edison's remake to go to the open market before AM&B's original. After the failed lawsuit, AM&B started selling their films soon after production. (By the way, the reason the lawsuit was ruled in favor of Edison was that AM&B had failed to copyright "Personal" as a dramatic work, in addition to their copyrighting the film as a photograph.) Back then, cinema was still a rather small industry and a new one for which laws were being created and adjusted. Some numbers will give an indication of the size of the movie industry. In the lawsuit, AM&B claimed damages of $3,000. This Edison film was the company's biggest hit of the year, for which they sold 71 prints in six months and 85 complete prints total in 1904-1905 (Musser).
Although it's near identical to "Personal", there are some differences between the two films, although I had to look closely at the two to see them (thanks to a handy dual purpose VCR and DVD player). AM&B's film consists of 10 shots, and Edison's consists of nine plus an expositional title card at the beginning. Additionally, "Personal" features nine women pursing the French nobleman (actually, I counted 10 during the scenes at Grant's Tomb, but one of them apparently gave up after that). Porter one-upped the original, with 11 women (although shot 5 appears to discontinuously include only 8 of them). Since both films show every character enter and exit the frame of each shot, the addition of two women is probably the main reason why the Edison remake is close to twice as long (675 feet compared to 371 feet).
Because early chase comedies generally repeated the same set-up of the chase in each shot-just changing the obstacle that the pursued and pursuers faced-in addition to showing every character enter and exit the frame in every shot, the scenes were mostly interchangeable, almost self-contained units. Thus, in the Edison film, the characters scale over a steep embankment in shot five; while in 'Personal', the characters perform a nearly identical act, but do so in shot eight. Other near identical scenes include the initial meetings and beginning of the chase at Grant's Tomb, the crossing of a bridge, and the climbing of a fence. For the remake, Porter dropped some of the less interesting shots and added an opening medium shot of the French Nobleman checking for his ad in the personal column while standing in front of a mirror, and he changed the ending. Originally, the nobleman was forced to marry at gunpoint after being caught behind some bushes, which was probably more comedic and certainly more violent. Porter changed this to one of the women being willing to walk through a body of water to catch her soon-to-be-husband: sweeter, if not as funny.
Next, Porter and Edison made a near-identical remake of AM&B's chase film "The Escaped Lunatic", re-titled "Maniac Chase".