Short answer. Generally yes. Article 1939 of the Civil Code provides that the members of the bailee's household may make use of the thing loaned, unless the agreement prohibits it or the nature of the thing forbids it. Your wife and children are household members, so they can use the vehicle unless your lender said otherwise.
What the law says
the members of the bailee's household may make use of the thing loaned, unless there is a stipulation to the contrary, or unless the nature of the thing forbids such use.
Civil Code, Article 1939 — Commodatum Is Personal. Read the full provision →
The personal character of commodatum, and one exception
A commodatum is purely personal in character. The bailee — the borrower — cannot lend the thing to someone else, and cannot lease it out. These are the consequences the Civil Code spells out under Article 1939. But the law carves out one deliberate exception: the members of the bailee's household may make use of the thing loaned, unless there is a stipulation to the contrary, or unless the nature of the thing forbids it. The exception exists because a household functions as a unit; it would be artificial to expect a borrower to keep a vehicle in the garage unused whenever a family member needs to run an errand.
Who counts as a household member
The Civil Code does not define "household members" for this purpose, but the ordinary meaning covers persons who live under the same roof and form part of the borrower's domestic unit — a spouse, children, and possibly parents or siblings living in the same home. A friend who visits, a business associate, or a distant relative living elsewhere would not ordinarily qualify. The closer the connection to the borrower's domestic life, the more clearly the exception applies.
When the exception does not apply
Two conditions can close off the household-member exception. First, a stipulation to the contrary: if your loan agreement — even a verbal one — said the vehicle is for your use only, then your wife and children using it would breach the agreement. Second, the nature of the thing: if the object lent requires a special license, special skill, or has an intrinsically personal purpose, the nature of the thing may itself forbid use by others. A licensed specialized machine, for instance, may not be something household members can operate safely or legally.
Your responsibility as borrower for household use
Allowing your family to use the vehicle does not dilute your responsibility as borrower. You remain liable for how the thing is used and for its safe return. If your spouse or child damages the vehicle, you are the one who answers to the lender. The household-member exception gives your family the right to use the thing — it does not make them independently responsible parties to the commodatum. That burden, along with the duty to return the vehicle in good condition, stays squarely with you.