Her family lived outside the city 'proper'. [=lived in an area that was close to the city but was not actually in the city]
Please put your shoes in their 'proper' place. [=please put your shoes where they belong]
The children must learn how to behave 'properly' [='appropriately'] in church.
(..) back to the detective division at any moment, I will let you off this time with just a warning. Thank you, monsieur l'agent. But you must get yourself a proper license. - First thing tomorrow. - Try to do something about your filthy monkey. Oh, one moment. Allez, allez. Over there! (..)1975 The Return of the Pink Panther
(..) - It is against the "leau"... - for you to play your musical instrument. - The "leau"? - What? - You say it's against the "leau"? - Yes, unless you have a proper license. - What kind of license? A license that permits the playing of any musical instrument... in a public place for the (..)1975 The Return of the Pink Panther