First let us start with 2 movie, the Nasu series of movies are simple stories told during a single race following a spanish rider named Pepe Benengeli. The first one is one stage in the vuelta as the main character is fighting in a breakaway. The other one is following a single race in japan.
The first one (2003) is Nasu: Summer in Andalusia and the other one (2007) is Nasu: A Migratory Bird with Suitcase.
The second choice is a series called Over Drive. It follows a normal boy named Mikoto Shinozaki who is recruited to the schools cycling racing club, Shinozaki has never practiced any sport but soon notices he may have hidden talent for cycling.