... BUT I think there ought to be some more criteria

CRITERION 4

A trip of a length plenty of people would take

CRITERION 5

Part of the route with some operator *other than* SNCF

CRITERION 6

Some part of the trip where a short non-rail leg would help as a passenger, but all rail options are possible too

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Starting with 5, that basically means you have to have Paris - Lyon as part of the route, where Trenitalia competes with SNCF

That means your route has to be somewhere south-ish of Lyon to somewhere north-ish of Paris

Valence Ville also helps with 6 - in that a bus to the TGV station outside town is a useful additional way to complete the trip