I'm afraid crystal balls are in short supply these days. I'm not sure anyone can predict what, if anything, you will need to enter France from Ireland in 2 months.
It could range from "you can come as you wish" to "whatever your status you can't enter France without an imperious motive and you have to quarantine for 10 days", with "you need to be vaccinated" or "a negative PCR test is enough" in between.
The current situation is that you can enter France with just a recent PCR test (and a sworn declaration that you don't have symptoms, haven't been in contact with a confirmed case and that you accept a test on arrival), and vaccines actually currently don't exempt you from that requirement.
Current details are here: https://www.interieur.gouv.fr/Actualites/L-actu-du-Ministere/Certificate-of-international-travel#from2
The current plan is to allow fully vaccinated persons to enter without the PCR test.
Note that this can change very quickly, as it has happened multiple times, most recently with additional restrictions for the UK due to the spread of the Indian variant there.