There are certainly flights from Paris to Nice, probably from both Orly and CDG airports. Check skyscanner.com for intra-European flights. Remember that carry-on baggage allowances may be very, very restrictive in terms of both size and weight. You'll probably pay extra to check bags, make seat reservations, etc., but it may still not be very costly.
The fastest trains take about 6 hours; that's what I'd prefer, because I hate trekking out to an airport in the middle of a trip, making sure I'm there at least 2 hours before departure for security procedures, etc. Check rail schedules on the SNCF website. Use your planned travel date and be sure to set the time of day. You'd be departing from the Gare de Lyon. I see a wide range of fares for the random May date I chose. You can probably save a lot of money on the train tickets if you buy them now, but there may be fees if you need to change the departure date or time. Click on the fare block for information about those policies.
Get Your Guide is a third-party company that connects travelers with tour guides (or tour companies, I assume) in many different places. I don't believe GWG actually conducts tours itself. Of the four destinations you mention, three (Antibes, Monaco and Cannes) are extremely easy to visit by train. The regional train running along the coast runs frequently and is inexpensive. Eze is a bus ride from Nice. I can't imagine enjoying a tour that rushed me through those four places on one day. It's just not enough time. Even if it were, what are the chances the way the tour company divvies up the time would match your preferences? Incidentally, some people enjoy Monaco (it does have quite a few visitable sights); others don't care for it at all. I haven't been there, so I don't have an opinion.
Rick has a guidebook focusing on southern France. I'd recommend getting a copy of it, reading about the area around Nice, and deciding what you most want to see. Except for St.-Tropez (which has no train station), nearly all the coastal spots are easy to visit independently by using the train. If I were going to take a bus tour, I'd prefer it cover places not so easy to reach on my own. Eze-le-Village is one example. St-Paul-de-Vence, Vence and Tourrettes-sur-Loup are others. Note that all those places do have bus service; it's just infrequent enough to make it hard to visit more than one or two of them on the same day.