It is an English name and most likely has no Irish Gaelic form.
The Irish name for France is an Fhrainc.
In Irish usage it is Carol as in English.
Spideóg is the Irish name for the bird known in English as a robin.
In Irish Rachel is the same as in English.(The Scottish Gaelic Raonaid is equated with Rachel, however.)
Aine is the Irish (Gaelic) for the English name Ann or Anne
Brianna is not an Irish Gaelic name. It is a feminine form of Brian in English.
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.
In the Irish language, they call it Gaeilge, and in the English language they call it Irish.
I can't find any instance of an Irish Gaelic spelling for the name therefore it would be the same spelling as in English.
Irish Gaelic, meaning pledge, or promise