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: Oceania Nautica Aug 2016
Next: Cruise Maritime Magellan Nov 2016
Then: P&O Oceana December 2016
Then: NCL Jade August 2017
Golden, Grand(2), Caribbean, Royal, Sea(4+1 aborted)
Adonia(4+2), Arcadia, Artemis(2), Aurora(5), Azura(2), Britannia, Oceana(3), Oriana(12), Ventura(2), Victoria(5)
QM2(2), QE2(9), QV(7), QE, Caronia(2),
Oceania Nautica, Minerva, Minerva II, Fred.Olsen(8), NCL Jade, =X= Eclipse, HAL Ryndam, Aza.Journey