It is a good idea to visit Spain in March. If you would like to visit Pyrenees in March you probably may find good weather enough to ride, the south face of Pyrenees (it means, the spanish side) is always warmer than northern and very sunny in Mediterranean communities. Well, a sudden change of weather is posible anyway, it's Spring time. Spanish ski season finishes in the month of february in most ski resorts.
I advise you to learn some spanish, average Spaniards have very few knowledge of English, we appreciate any effort to speak Spanish and people is usually very friendly and wishful to help foreigners. Don't worry if your prononciation is not perfect,

you will always find someone else to help you
You have lots of nice destinations in northeastern Spain. Avoid riding your bike in cities like Barcelona or Valencia -a crazy experience- and crowded mediterranean coast towns, especially in Easter. Try better instead the funny twisted roads of inner spanish country!
Here you are some ideas near of the border of France:
I suggest you to visit Besalú, in Girona, and the volcanic country of Garrotxa. They are all full of history and nice roads to ride
Besalú . Ciutat Comtal -
Territori i Natura - Turisme Garrotxa -
Another good idea is to ride more far in the south and visit Tarragona city
Tarragona Patrimoni - Informació de la Ciutat - Ajuntament de Tarragona , Unesco World Heritage and its inner countryside, like Priorat country
Consell Comarcal del Priorat - Web de Turisme, full of wineries and old monasteries.
More far away, in northern Castellon country you can follow the Templar Knights steps for example in Maestrazgo towns
Parque Cultural del Maestrazgo like Morella
Morella, Castellón and enjoy its perfectly twisted roads.
Just some ideas. Whereever you come to Spain you will find good reasons to ride a bike and sun, sun and sun!