Short answer. No. The Code allows a deposit to be made orally or in writing, so leaving something with a friend for safekeeping on nothing more than a conversation is a real contract. Writing is not what makes it valid — it is what makes it provable when the arrangement goes wrong.
What the law says
A contract of deposit may be entered into orally or in writing.
Civil Code, Article 1969 — Form of Deposit. Read the full provision →
Form is free, but delivery is not
The article settles the question of form and nothing else. There is a separate requirement that catches people out: a deposit is not created by agreement alone but by the handing over of the thing. A promise to keep something for you is binding as a promise, yet until the item is actually delivered there is no deposit and none of the keeper's duties have started. So the two questions to ask about any arrangement are what was agreed and whether the thing changed hands. Nothing in the Code requires a receipt, a signature or a witness for either.
Why writing still decides most disputes
Validity and proof are different problems, and it is the second one that ends up in court. An oral deposit is perfectly good law, and perfectly useless if the other side says the item was a gift, a sale on credit, payment of an old debt, or a loan he was free to use. Those are the arguments that actually get made. A short written record is what keeps the conversation on the facts rather than on whose memory to believe, and its value is highest precisely where people think it least necessary — between relatives, close friends and long-standing neighbours.
What a useful record contains
It does not have to be a contract drawn up by anyone. A dated note or even a message thread that identifies the item with its serial or plate number, records its condition, names both parties, states that it is being left for safekeeping and not for use, and says how long and whether anything is being paid, will do the work. Photographs taken at handover are worth as much as the words. Whether anything is paid deserves particular care, because a paid keeper and one doing you a favour are treated differently in several places in the Code.
What the keeper owes either way
Whether the arrangement was spoken or written, the duties are the same once the thing is delivered. The keeper must look after it with the care of a reasonably prudent person, must not use it without your permission, must not hand it to someone else for keeping unless that was agreed, and must return the very item, with whatever it has produced, when you ask for it. An oral deposit does not give him a lighter obligation. It only makes each of those obligations harder for you to prove — which is why the absence of paper is the depositor's problem far more often than the keeper's.