When do CIV conditions for delayed travelers apply?

CIV (International Convention for the transportation of Passengers, established by OTIF) rules apply in most European countries and a few nearby countries. In particular, under CIV rules, if the train operator is responsible for a delay on one leg of the journey, then the passenger must be conveyed to his destination in a reasonable manner at the carrier's expense (I'm simplifying here but that's the gist).

The treaty that establishes the CIV rules only applies to international journeys. (Some countries have similar rules for internal journeys.) Does it apply to journeys within a country as well, if there is an international connection? In particular, suppose I book trains, say, from Paris to Frankfurt with SNCF and from Frankfurt to Berlin with DB: if I miss my connection in Frankfurt, am I entitled to jump onto the next departing train (or to a hotel night if I miss the last train for the day)? Or the other way round (delayed national journey, then international journey booked through another operator)?