Is it all booked in one ticket? Or did you book multiple tickets?
As a general saying, if a train was late, and the entire journey is part of one ticket, and the connection was not possible within the minimum connection time due to the delay, you are allowed the next possible connection.
If you miss the train because you were loitering, it is your fault and you must buy a new ticket.
If you were to book a saver ticket to Paris to Basel SBB and another from Basel SBB to Bern or beyond, these are two different contracts and two independent journeys; consequently, when travelling from Basel SBB you cannot claim the train from Paris was late and therefore you could not catch the train as stated on the Supersaver ticket; thus, you must buy a new ticket from Basel SBB.