Well, slightly...
I happened to take the Paris Est - Strassbourg - Basel route myself last monday, albeit coming from the Netherlands instead of London (but still arriving at Paris Nord, so not that much difference).
Paris to Strassbourg was a TGV inOui ran with an ancient and worn trainset. Though the seats had seen better times, they still were quite comfortable in first class. (Even seat 61 where I happened to get allocated)
From Strassbourg to Basel the carriages are also really old, but there seemed to have been some kind of refurbishment inside as they looked less worn there. And where incredibly comfortable.
In Basel the French platforms are quite a walk from the main station concourse, so allow plenty of time for that.
Was a bit frustrating for myself as I actually exited the train under the Margarethenbrücke (where my hotel was right next to), but had to walk all the way to the main concourse and then back again
Basel to Strassbourg is running an half hourly service most of the day, so there almost always will be a quick connection available. I found much more options myself via that route than direct from Paris to Basel, the latter having the advantage of arriving in the main station.