According to voyages-SNCF, Eurostar is included on the Interrail travel pass. However, there is a booking fee of £26.50. That also might be subject to an extra £10 handling fee. The "Cheap flights" song suddenly starts up in my ear-worm generator.
You can take bikes on the Interrail pass as well, but let them know you are taking a bike at the time of booking.
PS I have just bought a 4-days-in-one-month Interrail pass for France, starting 20th May. £161 including postage of £10 (express delivery).