Hi Anne, good to see you are still interested in genealogy. You contacted me via the Sennett/Sinnott/Synnott surname study some time ago.
Had you thought more about getting one of the male members of your family (maybe your brother?) to take a Y-DNA (male line) test? I think this is still the best way to try to connect your whole family line back to the main Co Wexford line (the line that that is described in Burke's Irish Family Records, and goes right back to the 12th century and the very beginning of surname use, with the first of the anglonorman Synad/Synnot to arrive in Ireland). Good paper records just don't exist to take the line back to France, so DNA really is the best bet.
Just recently there have been two more people in the DNA project whose trees have now been linked back to this original Co Wexford line, so the DNA project is really starting to give results.
I was originally advising that the minimum test should be the YDNA37, however if this is too expensive for the moment, purchasing a YDNA12 test (this is only available if you get it by joining the Sennett DNA project page at familytreedna.com) should give enough information to know whether an upgrade would be worth doing later. The YDNA12 is about $58USD at the moment (the YDNA37 normal price is $169), so its a lot cheaper.
If other S-NN-T male descendants are reading this, then that last paragraph applies to any direct line male descendant of any family group that is believed to have originated from Ireland - obviously the more markers the better for good matches, but in this project if a 12 marker test shows the right E haplogroup, then we can still do some interesting analysis and preliminary matching.
This is the link to the DNA project
https://www.familytreedna.com/group-join-request.aspx?group=Sennett&vGroup=Sennett - click on PURCHASE A TEST TO JOIN THIS PROJECT, then scroll down to the YDNA section and choose whichever level of YDNA test you want (from 12 markers to 111 markers)