On TER trains, your bike travels free of charge, suspended or placed in a space provided for this purpose. These locations are accessible subject to availability and cannot be reserved.
The best summary in English at the moment is probably Taking bikes on French Trains - A Guide for Cyclists - Freewheeling France – https://www.freewheelingfrance.com/planning-a-trip/bikes-and-french-trains.htmlI think that’s out of date, sadly.Each TER region now has its own bike policies and some require reservations for certain trains, particularly in the summer months. Last May I took a TER from Caen to Tours and had to get a (free, online) bike reservation in advance.
The SNCF app and website are awful and often give incorrect info about both bikes and TERs, let alone the combination.Just used the SNCF app to see how to get a bike from Paris to the coast. You can do Paris-Dieppe but Paris-Calais seems impossible.
Always have a backup plan for any transport, if you can. I've been part of a 11 person group using two Dutch intercity trains in a tour and they are surprisingly bad, similar to TER trains, 6 bikes per train, reservations impossible, plus unlike TER, you have to pay for bikes. I think we allowed to miss six trains, if needed, but there was only one we couldn't fit the planned people onto. It felt like a minor miracle it worked as well as it did. I'd use trains again, but try to minimise the number, especially with a large group, and have a backup. Ideally, I'd ride the whole way, but I don't have that much time at once and some people I tour with have less.FWIW, four of us with bikes were refused entry for a train from Die to Gap, as they only had one space. No reservation possible, no refund either. Wouldn't ever bother with a group again, as too risky.
Not me but I float the option to you of the ferry alternative: Dieppe-Newhaven. Fare from Paris way cheaper and Newhaven may be more direct for you than Calais if cycling on or a straight train to Victoria (shorter than from Dover). I have taken the train both ways Dieppe>Paris (no reservations, plenty of space, avoid rush hour obv, changed Rouen iirc) and also ridden the Avenue Verte south from Dieppe. Ferry takes 4 hours and iirc cost me £32 (bike, one way) last September, rolling up no ticket.