The nearest opposite to sensible, if you are talking about a person's character and behaviour, is probably silly. If sensible means reasonable, moderate and governed by logic, silly is more or less the opposite.
Another possible opposite is senseless. While this can mean unconscious ("He lay on the ground for hours, quite senseless"), when referring to an idea, plan of action etc it means "Without sense/ logic/ reason." So the opposite of a sensible idea could be a senseless one; but you wouldn't describe a person as senseless, so in this case the opposite would be silly.
There is actually a word insensible, but this is very rare nowadays. It means lacking in feeling, empathy and so on (this is based on the old word sensibility, which means finer feelings/ emotions.) However, I don't think this is the word you want.
Another possible opposite is senseless. While this can mean unconscious ("He lay on the ground for hours, quite senseless"), when referring to an idea, plan of action etc it means "Without sense/ logic/ reason." So the opposite of a sensible idea could be a senseless one; but you wouldn't describe a person as senseless, so in this case the opposite would be silly.
There is actually a word insensible, but this is very rare nowadays. It means lacking in feeling, empathy and so on (this is based on the old word sensibility, which means finer feelings/ emotions.) However, I don't think this is the word you want.
