"I cannot relax!"
The English sentence emphasizes that one's body cannot be relaxed. Even though the context is not clear to its meaning, the definition seems to imply 休息 (to rest [literally]), which is close to 放松.
放心 is used for mind part and not the body. Even though 放心 and 放松 both have the common English meaning "to rest/to relax", 放心 refers to "to be [or feel] relieved/to have a peace in mind". For instance,
Do not worry! Just leave it to me.
However, since 心 is a noun, 放心 altogether can mean "indulgent mind".