Identifying a PS1 RPG with Blue-Haired Protagonist by Squaresoft: Chrono Cross

You are likely thinking of Chrono Cross.

• Protagonist: Serge, who has distinctive bright blue hair.
• Developer: Square (now Square Enix).
• Platform/Release: PlayStation 1, released in 1999.

It's a classic JRPG featuring a time-travel narrative, a large cast of recruitable characters, and a renowned soundtrack by Yasunori Mitsuda.