This will be a busy period for trains as most people visit their family during that time. Book trains requiring reservations well in advance (ASAP for some connections).

Spain is the worst place for Eurail as the vast majority of trains require a reservation (not always available online!) limiting your flexibility. However as soon as you've crossed the border it will be easier.

To get into France :

- IC train to San Sebastian + Euskotren across the border to Hendaye (not included, 3-4€) + TER to Bordeaux or towards Toulouse

- regional trains Barcelona - Portbou - Perpignan and further : quite long but scenic along the coast

- TGV from Barcelona to southern France : 25€ mandatory reservation

- AVE from Madrid/Barcelona to Marseille/Lyon : 10€ reservation, only available at RENFE ticket counters

After the crossing either you take high-speed trains (mandatory reservations in France and Italy) or slower reservation-free regional trains. Availability the day before in Italy is rarely a problem as trains run often. Switzerland and Germany have optional/no reservations. :)

Have a read at :

https://www.seat61.com/how-to-use-a-eurail-pass.htm

https://www.seat61.com/interrail-and-eurail-reservations.htm

Feel free to ask further more specific questions.

There are some long distances to cover here. At best you will need all day to get to most places you want to visit, more likely two days. 

I don’t think Madrid is a practical base for quick visits to Italy or Switzerland by train - even with the reservation problem.

I would be tempted instead to visit different parts of Spain, And maybe Bordeaux and Perpignan in France. And buy tickets for cash in advance, instead of using a pass.