Short answer. Often yes. The Code treats a guest's effects in a hotel or inn as a necessary deposit and makes the keepers answerable for them as depositaries — provided the hotel or its staff were given notice of the effects you brought in, and you took the precautions they advised for looking after them.
What the law says
The deposit of effects made by travellers in hotels or inns shall also be regarded as necessary. The keepers of hotels or inns shall be responsible for them as depositaries, provided that notice was given to them, or to their employees, of the effects brought by the guests and that, on the part of the latter, they take the precautions which said hotel-keepers or their substitutes advised relative to the care and vigilance of their effects.
Civil Code, Article 1998 — Hotel-Keepers as Depositaries of a Guest's Effects. Read the full provision →
Why a hotel guest is in a stronger position than a friend leaving a bag
The Code calls this a necessary deposit, and the word carries the reasoning. A traveller does not get to choose a trustworthy custodian, inspect the locks or negotiate terms. He arrives tired in an unfamiliar town and must put his belongings somewhere. Because he has no real alternative, the law does not wait for a contract of safekeeping to be agreed — it treats the hotel as a keeper of the guest's effects by operation of the statute. That is why a claim against a hotel does not depend on finding a clause in the booking confirmation about the security of your luggage.
The two conditions attached
The responsibility is not unconditional. First, notice of the effects brought by the guest must have been given to the hotel or its employees — the staff must know, at least in general terms, what is being brought in. Second, the guest must take the precautions the hotel or its people advised regarding the care of those effects. If the front desk asks you to place valuables in the safe deposit facility and you leave them on the bed instead, you have not met the condition. Both requirements point the same way: use the hotel's own systems and let its staff know what you are carrying.
What a disclaimer on the wall is worth
Very little, and guests should know that before they concede a claim. Notices posted in rooms or printed on registration cards announcing that the establishment is not responsible for lost articles do not, by themselves, undo the responsibility the Code imposes. Establishments also answer for the acts of their own employees, and the mere fact that a stranger did the taking is not automatically an excuse. Where the loss results from armed robbery or comparable force, the analysis is different. But a hotel's first response is usually the sign in the lobby, and the sign is not the law.
What to do on the day
Report the loss to the management immediately and ask for a written incident report with a reference number; a complaint made at checkout, or after you get home, is much harder to run. Ask that door-lock access records and corridor footage be preserved, in writing, before they are overwritten. Report the theft to the police as well. List what was taken, with values, purchase records or photographs where you have them, and note who at the hotel you told and when. Keep your booking documents and any card the hotel gave you about valuables, because the advice printed on it is part of the picture.