"I am not in a church."
Translation:Chan eil mi ann an eaglais.
I fear you have fallen victim to the received attitude that was prevalent in the past that 'peasant' languages are more likely to borrow from 'educated' languages than the other way round. See my comment here for historical attitudes to where words come from.
Ironically, given this particular example, it was the Church itself which was instrumental in establishing the 'order of prestige' where they preferred to believe a word came from a language higher on the list, without or despite the evidence. You will see that the beginning of this list is the order of languages through which the Word of God was brought to us. It is approximately
West Germanic languages
North Germanic lnaguages
Romany and Celtic
Contact between the French and the Gaels was largely limited to military alliance and there is little evidence of linguistic interchange in either direction. In fact there are far more words in Welsh and Scots of alleged French origin than there are in Gaelic, although many of these turn out to be Latin anyway.
In the case of Christian terminology, the early Church used Greek, and later transferred the vocabulary into Latin, so most of the terms are Greek, Latin or Latinized Greek. They took the same words with them wherever they went so it is not surprising there are many similarities.
- French église
- Old Irish eclais
- Irish eaglais
- Manx agglish
- Scottish Gaelic: eaglais
- Welsh eglwys
+ dozens more
See my answer here for a discussion of the other word for a church.
As for whether there is any other word for a church, there is no other word used for a modern church, but the word cill (related to a monk's cell) is used historically to refer to the 1st-millennium Celtic idea of a church that would be much more like a monastery or a priest's house than a modern church. This is very common in place names, and you can generally assume this is the origin of any name beginning with Kil such as Kilmartin, Kilsyth, Kilmarnock, Kilmalcolm etc. with the second element ususally being a saint's name.
Some people in Ireland say that the word eaglais, when referring to the building, has been completely replaced by the Irish for 'chapel', 'temple' or 'people's house', but I suspect this depends on the religion of the informant.
The religious groups that prefer the word chapel to church in English generally do not have a significant presence in Gaelic-speaking areas.