Sir James Fagan - Was James Fagan a son of Christopher and Mary Fagan?

From Christopher T.F. Fagan b. 1935.
Although I see that this post was made 10 years ago, I felt it might still be worth replying. I assume that the Christopher 1649-1740 who married Mary Nagle 1677-1747 are the two you mention in your first line. If so, they had 4 sons, of whom 3 died without issue, none of them named James, and the remaining one was Patrick 1696-1770. I am also descended directly from Christopher and Mary through Patrick and his son John of Kiltallagh (b. 1742). My substantial family records do not recognise the James you mention and I have never heard of a Sir James.
However, there are actually four Fagans who have been knighted. The first (and second) were Sir Hugh knighted by King Richard II in Dublin in 1399 and his son Sir John. Much later on Sir Patrick Fagan KCIE 1865-1942 was very senior in the Indian Civil Service, and finally there is Sir David Fagan KNZM b.1961 who is a well known person in New Zealand.
There was also a Chevalier Christopher Fagan 1733-1816 who was born in Ireland and entered the French army in 1755 in which he gained his French knighthood.
I hope this is of interest.