Searching Tyrgan Family in Ireland related to Normandy

Hello,
                 I'm from Normandy and I do genealogy with my mother (who's been doing genealogy for more than 20 years). Her grandfather's mother's name is Azélie TRIGAN born at Saint-Germain-des-Veaux in 1864.     

              Here is the story: A man named Maxime Trigant De LaTour born in 1875 wrote a book about our family.  He was a baron and (I think) a historian. He wrote in there that our family name is from Ireland, he wrote in French that the family is descended from Edward Tyrgan (called Trigant) who is (from his sources) the natural son of Henry III of England and a great Irish woman, Lady Tyrgan. He wrote they all came to France with King Henry and that this would be their crest: 
https://fr.geneawiki.com/wiki/Fichier:Blason_-_Famille_-_TRIGANT.png?mobileaction=toggle_view_mobile

       I wonder if by any chance, some of you would have any information about this family, I have been searching for months about them on Irish websites and so on. I even consulted the online archives and tried to search with the different orthography of the name (Tyrgan, Tirgan, Trigan, Trigant, Trigand, Tiregand) but in vain.    

        Elisée Reclus, a famous geographer also wrote a book where he mentioned the Tirgan family. He said that another source says that Edward Tyrgan was the son of Edward the Black Prince and not Henry III, which makes more sense. Because Edward Tyrgan built a castle in Aquitaine and the Black Prince had many lands there and spent 16 years living in Aquitaine. It would make sense that he gave land to his son and also that he met an Irish Lady because his father was a Lord in Ireland. On top of that, I've read on British websites that Henry III was very pious and had no known mistresses so there are fewer chances that Edward Tyrgan was the son of Henry III.

         I don't know what to believe, honestly. It seems vague and we have no information whatsoever about this Lady Tyrgan, except that she was an Irish noble. Edward Tyrgan's castle still stands nowadays in Aquitaine, it's named "le Château de Tiregand".  https://chateau-de-tiregand.com/chateau/?lang=en     
         It was built and rebuilt over the original castle over the years.

        So far, the only thing I found in Ireland is the location Tirgan, I thought it could be the beginning of a trail. I'm the only person in my family who speaks English so I'm doing research abroad but it's hard to find anything. If you could help me, I would be extremely grateful. Even learning a bit about this location could be interesting.  I don't know who to contact in Ireland or where to search.

 I thank you in advance and I wish you a lovely day!

Hi Wendy,

First of all, it's great to see that you are so passionate about your family tree. Congratulations for the research you have done so far. :) 

As you explained, the Trigant/Tyrgan family seems to be of noble ascend. That may explain why we didn't find anything on the pre 1866 surviving church records in Ireland. It's also possible that some corresponding records have been lost. 

Since the historian explained that the family came from Henry the 3rd and another from Edward the Black Prince and then settled in France, it seems like this goes way past our usual resources and records from the past 250 years or so. I also got my hand on the book by Maxime Trigant de la Tour, and very little is said about Lady Tyrgan from Ireland.    

Hopefully you get to find out more about your family, through literature, French or even English records (birth, marriage) before you get to the Irish side of it. 

Bon dimanche,
Antoine