There's no particular evidence that the song has any allegorical content, so I'd think any connection with Napoleon or Cromwell is no more than speculation. The Penguin example (see link above) was learned from an itinerant tailor "some time between 1804 and 1807", and that is the earliest date we have for it, though it was presumably at least a bit older than that. When you get back to the 18th century, the form of the melody isn't so very different from a lot of other songs of the period; a French connection is perfectly possible, but unnecessary to explain the way it sounds. The scholar Anne Gilchrist thought that it was related to the 'Spanish Ladies' tune.

The song seems unlikely to date back as far as the Civil War, but it appears to borrow elements from older songs such as 'A Bloody Battle Between a Taylor and a Louse' and the earlier 'A Dreadful Battle Between a Taylor and a Louse' which was printed c1655; so that may give it the air of greater age.

For the 'Dreadful Battle' (and a link to 'The War-like Taylor,' a slightly later re-working of it) see  http://www.folk-network.com/miscellany/penguin/bowmaneer.html