south of france/ questions from bernie

From Nice, I suggest that you plan to fly to Portugal and some other further destinations, which can be both faster and cheaper; see www.skyscanner.com. Trains along the coast of France are not as fast as the main lines serving Paris. Trains from Nice to either Rome or Barcelona, for example, take about 9 hours. Rick’s Train Travel Time & cost Map gives you an overview of faster trains at regular, 2nd-class fares.

Advance-discount fares can be much cheaper, if you lock in nonrefundable train tickets up to 3 months ahead. You can't really compare the value of a rail pass until you've laid out a firmer trip plan. Pass choices will be for 1, 2, or 4 countries and for a travel window of two months, that starts when you activate it at a train station.

We found an apartment in Nice for a week this coming summer on VRBO.com, and have used them with great satisfaction in other places, too. Their sister Website is HomeAway.com. We've also used Gites de France (www.gites-de-france.com), but even the English translation pages can sometimes have some info in French only. An advantage of April-June is that they're outside of the really high-demand season (July and August), so availability and prices on these Websites may be better for you -- but start looking right away.

What is the $5000 supposed to cover? For two people that would be a slim budget for a month. In the Nice area you would be close to the Nice airport with multiple connections. Lisbon would probably be more affordable. Remember, in the Schengen countries you will be limited to 90 days, not three months.

Try lodgis.com for Nice. We've used them for Paris. Good luck.
http://nice.lodgis.com/

I'm concerned that the flat may have limited availability during the second half of May when every hovel within about 50 miles of Nice and Monaco is hired for ridiculously high prices by the circus (very fun circus, but a circus nevertheless) of the many many thousands of people associated with the Monaco Formula One weekend, both fans and officials and teams. After the Sunday of the race everything goes back to what passes in those parts as normal. I have been there as close as the Wednesday after the race and everything is normal except that the stands and Armco barriers are still there, as well as the rubber on the road.

But the 2 or 3 weeks leading up is a madhouse.

I'll be there in March, and that will be lovely and "quiet".

Unless you have special citizenship 90 days is all you can do on a Schengen visa waiver program, not "3 months". That includes arrival and departure days. All the countries you have named are Schengen signatories.