Here's a start. All are free to read online.
1) This is published by Catholic University of America (which may or may not give it a truly Catholic perspective): Aston, Nigel.
Religion and Revolution in France, 1780-1804 (Catholic University of America Press, 2000).
https://archive.org/details/religionrevoluti0000asto2) French historian Reynald Secher's 1986
A French Genocide: The Vendée, though it seems limited to the Vendee rather than the Revolution overall.
https://archive.org/details/afrenchgenocide.thevendeereynaldsecherv3) Here's a dissertation that's probably written in an attempt at academic neutrality, though we know there's no such thing. At the very least it can give you an overview of what arguments to look for that can be refuted from a traditional perspective, and a discussion of Gallicanism necessary for understanding the topic as a whole. Harmon, Joseph Peter.
Nation and Church in the French Revolution. The Florida State University, 2021.
https://diginole.lib.fsu.edu/islandora/object/fsu:803246/datastream/PDF/viewProbably in general, some of the better works are still not translated, so if you can read French, that would be an advantage. If so, try the lists of sources provided at the end of each of the above.
A caution: some contemporaneous writers of a more seemingly theocratic leaning might have written less from faith and more out of political-sociological interest. For this reason, authors such as
Joseph de Maistre or
Felicite de Lamennais might be useful more for historic context than for actual Church-centered analysis.