You need que in this context, because it functions as the introduction of a subordinate clause and not as a relative pronoun.

Nous pensons que c'est une bonne idée. -- We think that this is a good idea. (Note that "that" isn't a relative pronoun in the English language version either.)

Ce que tu dis est une bonne idée. -- What you say is a good idea. (What = that which)

Claudine aime tout ce que son père lui dit. -- Claudine likes everything that her father tells her. (that = that which)

Claudine aime que son père lui raconte des histoires. -- Claudine likes that her father tells her stories.

Notice that in the last case, where "that" isn't a relative pronoun, the substitution by "that which" doesn't work.