I'm not a native speaker so I'm not sure if it applies to the word "contract" that you are using, but in France a "contrat" exists as soon as there is a meeting

I'm not a native speaker so I'm not sure if it applies to the word "contract" that you are using, but in France a "contrat" exists as soon as there is a meeting of the minds. Writing it down and signing it makes it easier to prove to a judge, but it's not necessary.