My 3rd gt-grandfather, James McKenzie, was in the 21st Regiment of Foot (Royal Scots fusiliers, I think.) From what I can see of the regiment's history, they were fighting the French in the Low countries and then in Louisiana. At sometime during his service, he married (?) Agnes (surname not known). The first daughter was born at Liff, Angus c1816. I think he had returned to Scotland by then.
James McKenzie was a private. He enlisted in the Royal Fusiliers at Cookstown, Tyrone, Ireland in March 1800 and was discharged in July 1817.
Wikipedia says that the regimental barracks were in Ayrshire and the regiment took part in the Siege of Bergen Op Zoom in March 1814 and the battle of New Orleans in Jan 1815. (It might have been in Scotland, briefly, in between.)
James McKenzie's baptismal record, at Kirriemuir, in 1779, mentions his residence at Ballinshoe (the locals, apparently, call it Benshie).
It says that he had "received a contusion in a battery before New Orleans".
"Outline History - 21st Regiment of Foot" on GENUKI Ayrshire pages.
https://www.genuki.org.uk/big/sct/Ayr/Military/21stThere were 2 battalions during the wars against Napoleon's France. If James enlisted in 1800, went to America with the regiment, was in action at New Orleans and wasn't discharged until 1817, he must have been in the 1st Battalion.
2nd Battalion was raised at Ayr in 1804 on resumption of the war with France, following a temporary break in hostilities after the Treaty of Amiens. It was raised under the Defence Acts from men in Ayrshire and Renfrewshire. It remained on home duties for a decade, acting as a depot for 1st Batt. 2nd. Bn. then went to Holland and took part in the Siege of Bergen op Zoom in 1814. 2nd. Bn. returned to Scotland from Ostend 1815 and was disbanded at Stirling, January 1816.
1st Battalion went here, there & almost everywhere.
1795 returned to Scotland from overseas.
1803-1805 Ireland (according to GENUKI; need a source for presence in Ireland 1800)
c.1805 England
1806 Sicily
1807 Egypt
From Egypt to Italy again.
1812 Spanish coast
1813 Italy
1813-1815 America
June 1815 England
July 1815 Low Countries
1815-1817 (approx.) France as part of army of occupation
1817 returned to Scotland
(Timeline is from GENUKI source; need specific sources for collaboration & accurate dates.)
As you can see from the above timelines, the battalion which was at Bergen Op Zoom in 1814 was a different battalion to that which was at the Battle of New Orleans 1815.
James may have married anywhere, Ireland, Scotland, England, Europe, Egypt, America. May have been married by an army chaplain, or by a local clergyman in a local church, or possibly in a civil service while in France. He may not have had a formal marriage. What do you know about his wife?