Booking SNCF or IC Train from Paris to Bayeux with a Eurorail Pass

No need to book ahead—there are always seats. Also, the site may say you can book four months out, but they may not list all of the train options that far out. FWIW, I book with SNCF. They are the ones who actually operate the trains. Everyone else is just a reseller.

Do you mean that you have a Eurail pass? I have not heard of Eurorall passes so my answer is based on the Eurail passes. Your issue could be the fact that you have a pass. Passes can be a pain to use on French trains because the number of seats available to pass holders is limited. It is my understanding that you need a reservation with a pass for most French trains if you have a Eurail pass. The best way that I know of to get a reservation if you have a pass is to go to https://www.eurail.com/en/book-reservations#/ and book your reservation. The reservations may not yet be available for travel four months out but I suggest that you check every week so that if you need a reservation you can get one early because seats for pass holders are limited on French trains. The train may not be sold out but seats available to pass holders could be sold out. That is a lesson that my family and I learned the hard way.

As far as I know, IC (Inter-City) is a type of train operated by SNCF, not a different operator with its own website. I suggest this resource:
https://www.seat61.com/train-travel-in-france.htm

SNCF has Intercités trains, but does not call them “IC.” That is a term for, I believe, some German trains.

Went to the IC website and still no luck

which exact website?