Not sure about Bürkliplatz: if it's not now it'll be next week, once May has arrived.
Helvetiaplatz has it's Saturday morning flea market in operation again: good to go at the beginning of the season when all those eager-beavers have cleared out their parents attics. Plenty of gems amongst the tat. Also a good place for an openair haircut, mirror propped against a tree, people milling around you drinking rosé: cool