In France postcodes usually span several towns, or one medium city, and only larger cities have several postcodes (three for my 300 000 inhabitants city, for example).
They are not very precise, which is to be expected since there are only about 100000 possible postcodes in our scheme.
The US used to have five-digit postcodes, now has nine-digit ones, but laypeople mostly ignore the extra four digits. Singapore used to have two-digit codes, then upgrade to four, then to six. Maybe French postcodes will grow another digit or two someday.
The U.S. system is nice in that most people only even need 5 digits. The USPS reduces fees for their large customers that use all 9 digits, so they still end up with the majority of their mail being very specific, while those just sending a letter to a relative can just use the 5-digit code and let the destination post office take care of re-sorting it before delivery.
They are not very precise, which is to be expected since there are only about 100000 possible postcodes in our scheme.