@aloiscochard's comment is almost there. What he forgot to mention is that case class companion objects already implement the appropriate FunctionN
trait, so you can simply do this,
scala> case class StringCaseClass(argument: String)
defined class StringCaseClass
scala> case class IntCaseClass(argument: Int)
defined class IntCaseClass
scala> def method[A, R](caseClass: A => R, a: A) = caseClass(a)
method: [A, R](caseClass: A => R, a: A)R
scala> method(StringCaseClass, "foo")
res0: StringCaseClass = StringCaseClass(foo)
scala> method(IntCaseClass, 23)
res1: IntCaseClass = IntCaseClass(23)