Bonjour Ben! Where do we buy bus tickets for bus from St Supice church to Eiffel Tower. Do we buy them on the bus? Second Question: On Sundays, how often does this bus run? (We have a timed-entry to Eiffel tower.)
You can buy Paris city bus tickets directly from the driver, although they are more a bit more expensive (2.50€ vs. 2.10€ as of 2023) and cannot be used for transfers. It's better to buy a Metro ticket (which are valid for buses) from any Metro station ticket window or automated ticket machine and use those. Paris Metro tickets, known officially as Ticket t+, are valid for buses & allow transfers.
Regardless of which ticket purchase option, remember to validate the bus ticket by inserting it into the ticket machine on board and taking the ticket back and holding onto it until alighting.
Bus #86 from Saint Sulpice to Champ de Mars then about 4 min. walk to the tower is probably your easiest route. The bus should list "Champ de Mars" as its destination and you'll ride it right to the end of the line and get off there to walk the remaining distance.
Here's the Google Maps itinerary as an example.
Frequency of bus 86 from Saint Sulpice to Eiffel Tower is about every 15-17 minutes on Sundays. Your total travel time including walking will be 25-30 min.