The adjective you're thinking of is "shabby chic."
Explanation:
"Shabby chic" refers to a style of decoration or design where old or worn-out objects (or their aesthetic) are reused or repurposed, often with a modern twist, giving them a trendy, stylish appeal.
It can apply to furniture, interior design, and even fashion, but it is not typically used for buildings or areas.
For buildings or areas:
A more appropriate term might be "vintage-inspired", "retro-modern", or simply "revitalized." For towns or neighborhoods that maintain their historical charm while being updated for modern use, you could use:
"revamped historical district"
"modernized old town"
"restored vintage charm"
"heritage-inspired area"
For example:
"The old quarters of the town have been beautifully restored, maintaining their charm while incorporating modern functionality."