Proper Noun:
* When referring to the language specifically, it's a proper noun and should be capitalized: "I'm learning French."
* When referring to the people of France or their culture, it's also a proper noun: "The French are known for their cuisine."
Common Noun:
* When referring to the language generally, it's a common noun and should not be capitalized: "She's fluent in French and Spanish."
* When referring to things related to France, like cuisine or style, it's a common noun: "This restaurant serves French food."
In short, look at the context to determine whether "French" refers to a specific language, people, or culture (proper noun) or to a broader concept (common noun).