Look up British timetables on https://www.nationalrail.co.uk/

For international planning, use the DB planner.

Reservations for day trains in GB are always optional. They can be booked free of charge at a GB ticket office or online, see this post.

Eurostar (London - Paris) and French trains can be booked via Eurail (2€ booking fee per person and train) or by phone via SNCF: Press #85 for English, no booking fees, reservations are sent via e-mail.

IF you spend more time in FR-and I guess so, do not overworry too much-easiest way to get REServ-if needed at all (many lines can use slower trains without) is at FR SNCF machines-do it when you arr in FR and have plans fixed.

I doubt if a pass is rally worthwhile-in FR there are also cheaper advance fixed fares. And how do you get into Bangor? By balloon or landing from the moon? Railfares inn UK can be sky-high.