How can I save a json-encoded string with international characters to the databse and then parse the decoded string in the browser?
This is an encoding issue. It looks like at some point, the data gets represented as ISO-8859-1.
Every part of your process needs to be UTF-8 encoded.
The database connection
The database tables
Your PHP file (if you are using special characters inside that file as shown in your example above)
The content-type headers that you output