Paris to Lucerne to Florence and Barcelona to Madrid

First, you are looking at a total of 1,800 miles. Second, you don't indicate on which dates you will be traveling or if you actually will be flying into Paris and out of Madrid which is easy to do. The easy segment is Florence to Barcelona. The Spanish budget airline www.vueling.com has 1hr40min non-stop flights from Florence to Barcelona for as low as 59.99Euro. However, that's a hard fare to find unless you are flying in late August for September. If you are flying sooner, the fares will be higher as they are filing up. The sooner they fill up, the higher the fare.

Paris to Lucerne can easily be done by train. The journey takes 5.0hrs-6.5hrs with 1-3 train changes depending on when you travel and the time of day you want to travel. The French train website http://en.voyages-sncf.com doesnt' display Paris to Lucerne but I can see a very nice non-refundable fare from Paris to Basel SBB for 25 Euro. Basel to Lucerne is just another hour by train. That's a really cheap trip. Again, you haven't provided any information on when you will be traveling so we can't narrow this down.

Lucerne to Florence can also be done by train via Milan. This is a 5.5hr-6.5hr train ride with 1-2 train changes depending on the run you choose and the time of day you travel. The Swiss www.sbb.ch show a regular fare of 145CHF with a non-refundable fare of 91CHF. Flights are not practicable as you would have to return to Zurich. Budget airlines all have 1-stop flights in Germany or Barcelona. Swiss Air has a non-stop for almost $1,000.

Barcelona to Madrid is again best by train. The high-speed AVE train makes this journey in about 6.0hrs. You could fly this one on Vueling in just over an hour for as low a 55Euro.

Larry has great suggestions for Paris to Lucerne to Florence (I have no experience with Spain). I actually booked the same route fairly recently, except in reverse. If you can purchase right as the tickets come out (at 90 days in advance) you can get Paris to Basel for 25€, which is greatly discounted as it can cost above 100€ per person. For pricing on Lucerne to Florence, check both the SBB and Trenitalia websites. I sometimes find the cost is slightly cheaper on one or the other. You will find great discounts if you book far enough in advance. Tickets are non-refundable, non-exchangeable, but the discount can be worth it if you are willing to lock into a schedule.

Train makes more sense because otherwise you would have to travel to Zurich or another city for the airport, and that plus getting to the airport for security etc would add quite a bit of time - the train is more direct and brings you right to your destination.

In all these cases (except Basel-Luzern) you'll save money by locking in the best rates now (or up to 3 months ahead for trains). See http://www.ricksteves.com/travel-tips/transportation/trains/france-rail-passes#ticket-tips for advice on booking the Paris-Basel discount. Spain's advance-purchase discounts can be hard to book directly through Renfe and are not currently working on Rail Europe's web site, but you can get them at https://petrabax.com/renfe/tickets/.