Short answer. Only in two situations. Article 1982 presumes the depositary is authorised to open your locked box when it becomes necessary — but only if you delivered him the key, or if your own instructions about the deposit cannot be carried out without opening it. Absent either, opening it is unauthorised.
What the law says
When it becomes necessary to open a locked box or receptacle, the depositary is presumed authorized to do so, if the key has been delivered to him; or when the instructions of the depositor as regards the deposit cannot be executed without opening the box or receptacle.
Civil Code, Article 1982 — Presumed Authority to Open. Read the full provision →
A locked box signals the contents are private
Handing someone a locked box says something the law takes seriously: the contents are not for the holder's eyes. A depositary's duty is to keep the thing, and where the thing is a sealed or locked receptacle, keeping it faithfully ordinarily means keeping it shut. He is not entitled to satisfy his curiosity, to inventory what is inside, or to open it merely because it would be convenient. Article 1982 is the narrow exception to that expectation of privacy — it tells us the only circumstances in which the person holding your locked box may lawfully open it, and everything outside them remains off limits.
The two conditions, both resting on necessity
The article sets two conditions, and both begin from necessity: When it becomes necessary to open a locked box or receptacle, the depositary is presumed authorized to do so, if the key has been delivered to him; or when the instructions of the depositor as regards the deposit cannot be executed without opening the box or receptacle. The first turns on the key. Delivering it to him is read as trust that he may use it when opening genuinely becomes necessary. The second turns on your own instructions: if you asked him to do something with the deposit that cannot be done while it stays shut, opening it is the only way to obey you.
It is a presumption, not a free hand
The word doing the real work is presumed. The article raises a presumption of authority in these two cases; it does not grant a free hand. The presumption can be displaced by what you actually said — a depositor who hands over the key but expressly forbids opening has rebutted it, and the holder may not shelter behind the article. Nor does either limb licence opening on a whim: necessity still has to exist. Where you never delivered the key and gave no instruction that requires access, no presumption arises at all, and forcing or opening the box is a breach of the deposit rather than an exercise of implied authority.
What to check if your box was opened
So the practical questions are concrete. Did you give the holder the key, and if so, did you say anything limiting what he could do with it? Did you leave any instruction that could only be performed by opening the box? If neither is true and your box was opened, the holder acted outside Article 1982, whatever explanation is offered afterwards. If you want the contents kept sealed no matter what, the safe course is not to part with the key and to state in writing that the box is to be returned unopened — putting the matter beyond the reach of a presumption the law would otherwise supply.