I am so wrapped with everyone's replies.
Yes Wildermoth/Wildermouth does sound German and we always wondered if there was a connection. There are several Wildermuth's in Germany and the USA but as far as we know our Wildermoth/Wildermouths never spelt their name this way.
thanks so much for the information of Jean Henri and his wife. I think there is a strong possibly that these could be Jean Christopher's parents.
The name Jean appears in the family a few times, Jean Henri, Jean Christopher, J. William (first name was we think Jean) and so on. There is also the strong tradition of military service. Jean Henri, Jean Christopher, J (Jean) William all did long time service in the army and J. William's son John was a policeman (as was brother) and served in the Crimean War and one of his descendents died at Gallipoli.
There was a family rumour (which we know is never reliable) came from a town called Neufchatel. There are several towns in France and Switzerland with this name so have know idea which one or if this is true.
It is very exciting to think that there may be a Swedish and Austrian connection. The family seem to have been well travelled! (i.e. Sweden, Austria, France, Ireland, England, New Zealand)
I always thought we might of have been able to find out more through the wives but have virtually no information of these women either.
Jean Christopher married Anne Keenan
J. (Jean) William married Mary Whelan (have no other information on her)
John Wildermoth married Sarah Byrne (again have no information on her)
All I know is a rough age and that they were all born in Ireland.
I will try to follow up on the military record for Jean Henri and see if there is more information there as this does seem like a strong led.
Looking at the von Hugel connection I see that they were strongly Roman Catholic something that the Wildermoth's were also so again Jean Henri and his wife Marie Von Hugel are looking like good contenders.
There are several Wildermoths in New Zealand so the family has done well here. There does not look like there are any left in Ireland or England so perhaps this line died out? (how sad)
Thank you all so far for the information provided - it has given me a few leds to try to follow. I feel that I will be improving my French! to try and understand more. Here's hoping I can get Jean Henri's military record (cross fingers!)