Is there a direct flight from Nice to Venice on a budget airline?
Hedy,
According to www.whichbudget.com, Air Berlin showed flights from Nice to Venice however their website has no listings for these. It's possibly they've been discontinued?
One alternative might be to fly from Nice to Milan / MXP and then take the train to Venice. However, I'm not sure if this would save much time over using the train. The shortest rail trip I could find was 7H:47M, with two changes at Ventimiglia and Milano Centrale. By the time you travel to and from each airport, check-in, security, waiting and collecting luggage, the times might be fairly close (and for me the air travel would be more of a hassle).
Good luck and happy travels!