Global Pass Home country travel Question

I live in Cornwall Uk and will be traveling to France via the Eurostar from London to Paris. Below is an outline of the intended travel days:

Day 1: Cornwall → London → Paris

Day 2: Paris → Lyon

Day 3: Lyon → Montpellier

Day 4: Montpellier → Avignon

Day 5: Avignon → Nice

Day 6: Nice → Paris → London → Cornwall

My question essentially is whether I am able to make these multiple connections within my home country (Cornwall → London → Paris and Nice → Paris → London → Cornwall) on the global pass as the inbound/outbound days or would I need to but separate train tickets for the Cornwall → London and London → Cornwall sections? 

Thank you in advance!