The supermarket Petit Casino is open 'til 20h00, the Frogonard perfume shop 'til 18h00 and the rest (not many) are on this link :
http://www.les-horaires.fr/06360/Eze/
There may be others but I couldn't find them. If there are more, except for bars and restos they will close around 18h00/19h00.
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