I assume the family were RC. Unfortunately Inver RC baptism & marriage records don?t start till 1861, so if he was married there in the 1830s you won?t find a church record of it. (That?s not untypical for Co Donegal where few RC parishes have records for the first half of the 1800s.)
If James and Mary happened to have any children born in Scotland in 1855 or 1861 onwards, then the date and place of the parent?s marriage will normally be recorded on the child?s birth certificate (which you can get on the Scotlandspeople site).
If James & Mary ever claimed under the Poor Law (and many Irish residing in Scotland did claim), then their parish in Ireland will normally be recorded in the Scottish Poor Law files, often with details of family and next of kin. You don?t say where in Scotland they resided, but if it was in the Glasgow area then the Poor Law records for that area are in the Mitchell Library.
I looked for mentions of Irish fighting for the French at Waterloo. According to this reference, there was a Legion Irlandaise, but they didn?t fight at Waterloo, and were disbanded soon after.
Statistically, I would have thought he was more likely to have been in the British army, but obviously that?s just speculative.