Hi L2C, don't worry too much with any European city with regards to Sunday opening - especially if they rely on tourism & you visit in the peak of Summer, nearly everything will be open & very lively.
If you're not sure what to do in Villefranche, may I suggest taking a look at http://www.cruisecritic.com/ports/newport.cfm?ID=84
which seems to sum everything up quite nicely, with photos as well.
Whilst on the French Riviera, it is also quite easy to use the train service to visit other towns such as Nice & Cannes, or even another "country" with Monte Carlo/Monaco along the coast.
Hope you have a lovely time,
Alan & Katrina
Last Cruise: Azamara Journey August 2014
Next: Queen Victoria November 2014
Followed by: Queen Elizabeth December 2014 and Minvera April 2015
Golden, Grand(2), Caribbean, Sea(4+1 aborted)
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QM2(2), QE2(9), QV(5), QE, Caronia(2), Minerva II, Fred.Olsen(8), NCL Jade, =X= Eclipse, HAL Ryndam, Aza.Journey