Belle would probably think that Ariel is annoying

Absolutely. They are both curious and adventurous and I don't see why Belle would dislike Ariel's rebelliousness. Just because Belle has a great relationship with her very liberal dad, doesn't mean she believes everyone should obey parents unconditionally. It doesn't even she mean would have a great relationship with dad and would be an obedient daughter, if her father were more like Triton. Triton has traits Belle disliked about the Beast and traits she disliked about the villagers, why would she even side with him? Maybe Belle wouldn't approve Ariel making a deal with an obviously untrustworthy Ursula but she definetely would approve Ariel not agreeing with her father's mindset about humans and giving human race a chance.