No first hand experience, but some info based on online sources:
Looking at the airport website, you'd probably be taking bus 50 to Basel, which is operated by BVB (Basel's public transport company).
BVB's website has a page on single tickets which only talks about Swiss francs. However, you can also buy the ticket from a machine which accepts euro coins:
The new ticket machines not only tender the full range of available
tickets (multi-trip tickets, day tickets, group tickets, cross-border
tickets), they also offer cash-free payment (Postcard,
EC-Maestrocard); if you prefer to pay in cash, the machine accepts
both Swiss franks as well as Euro coins.
So, you'd probably get by with euros, assuming there's such ticket machine at the airport. Though maybe it's best to get some Swiss francs beforehand, just in case. (Or simply withdraw them after arriving at the BSL airport.) You're going to need them in Switzerland anyway.
Somewhat related, the airport FAQ mentions:
In the French sector of the airport, it is usual to pay in Euros, in
the Swiss sector in Swiss Francs.