I think it could be valuable, and destinations like Manchester and Birmingham could definitely provide adequate passenger levels
The thing is, they couldn’t as a stand alone international service. The entire daily flow between the North West (Manchester & Liverpool airports) the West Midlands (Birmingham airport) and Paris could comfortably fit on 2 eurostars each way (compared to 7-9 flights daily). Many of those air passengers would not be prepared to spend 4-5 hours on the train and/or pay substantially more for the journey and/or travel at the times the more limited train service would run. Some other passengers are travelling to Paris CDG to change planes to head further afield, so the train would be no good anyway.
If the servicewas essentially open calls everywhere, ie in Schengen, then it would be quite feasible to run a bi- hourly WCML* to Paris and bi-hourly ECML to Paris with a London call probably as a reverse at St P or possibly at Stratford. Albeit that would need UK gauge trains.
*not HS2