Plenty. There's three multistoreys within about 100 yards, but on-street parking should be fine on Sundays - not right outside the shop (that's disabled spaces) but on the street.
If using Satnav, do NOT use the shop's postcode (no satnavs seem to understand the complicated driving restrictions round here, and I keep losing delivery drivers!) Use BS23 1ST instead, which is the other end of the road and you'll (a) stay legal and (b) end up by a nice Japanese restaurant.
Directions: M5 J22 is easiest coming North, follow signs to Weston and you'll come out on the seafront. Follow the road along. Just after the Grand Atlantic Hotel (big spiky Victorian thing) you come onto a little one-way system - stick in the middle lane and take a right into the town (past big Premier Inn on the corner). This is Carlton Street, there's a multistory on the right if you want it. Otherwise take a left past all the demolition works then left onto Oxford Street, straight over the traffic lights and next right. That is St James Street, there's parking all down the left-hand side, and also on the next street on your left. They've just put meters in, but they don't apply on Sundays.
We're up at the Marks & Spencers end, directly opposite the White Lion.
(EDIT: Don't use Google Earth either - whole area's been remodelled since then and half the roads have been pedestrianised).