For a CDI contract the notice period should have been explicitly stated however for such a contract I would normally think that the notice period should correspond to one pay period, i.e. a month if you are paid monthly. I'm no expert though and the law may prescribe something different.
It would seem sensible to discuss this with theemployer's HR department and ask how much notice you have to give if you are serious about it, what's there to lose?
You don't say if you have worked a probationary period but my understanding is that you are allowed the time off to look for another job if they dismiss you rather than the other way around, so my understanding in the circumstances is that no you are not entitled to take leave to job hunt, nor does it make sense that you should be.
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