Once you kiss someone on the mouth, you become exclusive to each other unless you agree otherwise.
In French culture, it means you decided to commit to a relationship while becoming acquainted with that person.
When it's time to say goodbye, be direct with your explanation.
The French often meet their significant other through their social circle at group get-togethers rather than “date" people they hardly know.
The way the French respond to another's interest in them, their accepted behavior during courtship and how their relationships progress can baffle an American seeking love in France.
When social encounters with foreigners involve romance, your cultural makeup can trip you up if you don't know what to expect.