There is a Canadian email address on thepeerage for Richard Glanville-Brown who in 2005 contributed all that Christian information, including the children of Robert Oates Christian and Jane Sayle. One of the brothers (whether or not married) can be assumed to be the father of Caroline Jane Lucy Christian, b.France. Have you tried asking him where he obtained his information (rather meagre) about the children of ROC & Jane Sayle?

He does not give any of his sources, nor how he came to the conclusion that the 7 siblings he lists were all born at The Flatt, with the exceptions of Jane and Howard b.France.
We know that Thomas Philip Christian was born in London.
For child no.1 he writes:
"Robert Christian was born at The Flatt, Maughold, Isle of Man. He was the son of Robert Oates Christian and Jane Sayle. He died, unmarried. He was buried, at sea".
How does he know, amongst the dozens of Maughold Christians? Did he leave a will, and if that was the source why not give a date?

Jane Sayle Crellin als Christian is the only sibling he has dates for, and he confuses her birth year with that of her daughter's, to whom he gives no birth date.
He writes:
"Jane Sayle Christian Crellin was the daughter of Edward Crellin and Jane Sayle Christian. She died on 17 June 1927 at Ramsey, Isle of Man. She was buried in June 1927 at Kirk Maughold, Isle of Man.
During the last years of her life she lived with her niece, Caroline Jane Lucy Christian, but it is unclear who Caroline's parents were, as there is no other reference to her."

But Caroline was the niece of other Jane's mother Jane Sayle Crellin als Christian - the head of the household in 1891 & 1901 - not of her daughter (who d.1927).

Jane Sayle CRELLIN 84 yrs., Washington House, Ramsey, was buried in Maughold on 16 Feb 1917.

If Richard Glanville-Brown was correct about all Jane's brothers, you have 5 possibilities from whom to find out which was the most likely to have had a child born in France, and given to his sister to bring up.
(He doesn't seem to have picked up that she was b.France when he writes that there was no other reference to her.)

You could try wills. A decree for Robert died at sea, and John William "died unmarried" may name a niece ("daughter of"), and would certainly name a child of their own.

Children of Robert Christian & Jane Sayle:
Catherine Margarette Christian bapt Ramsey 16 Sept.1821.
Robert Oates Christian bapt Ramsey 8 Dec.1822.
John William Christian bapt Ramsey 14 May 1826.

I can't find the other one (plus Jane & Howard in France, and Thomas Philip in London).
Perhaps in France?
Matthew was the other possibility to be the father, if he was correctly one of the siblings.

You mentioned Caroline's death, but don't say when it was. Did you see her will? Did she mention anyone other than her cousin John Longford Lee Crellin Christian? As she named him perhaps he was her closest cousin, and she was Thomas Philip's daughter? Did he name her in his will?

You wrote "I have the will (May 15th, 1919) of Jane Sayle Christian Crellin who was a cousin to John Longford Mellor Christian". I might be confused with all these Christians, but wasn't she his aunt, if he was Thos Philip's son?

Sue