It is an English name and most likely has no Irish Gaelic form.
The Scottish Gaelic name MacEanraig would would be an equivalent.
In Scottish Gaelic Frangag is the equivalent of Frances.In Irish it would be Proinséas.
Rowan can be either English or Irish. The Irish surname was originally Ó Ruadháin. As a first name: Ruadhán.The English name can be found in: N. Lanarkshire, Warwickshire, Norfolk, and Greater Manchester.A rowan tree is caorthann in Irish. Scottish Gaelic: ?
Aine is the Irish (Gaelic) for the English name Ann or Anne
In English it is referred to as Gaelic (or Scottish Gaelic), a language related to, but distinct from, Irish (or Irish Gaelic).It is called Gàidhlig in Scottish Gaelic; pronounced 'gallic'.
You need to specify Irish Gaelic or Scottish Gaelic: they are two separate languages.
There is no special spelling of the name in Irish or Scottish Gaelic: it would be the same as in English.
I can't find any instance of an Irish Gaelic spelling for the name therefore it would be the same spelling as in English.
The spelling Carol is used.
Irish Gaelic, meaning pledge, or promise
The Irish equivalent of Denis is Donnchadh; Scottish Gaelic: ?