While we always capitalise the first letter of all countries and nationalities in written English, the same cannot be said for written French. While in French, countries are also always capitalised, whether nationalities should use capitals depends on the context.
When speaking about a person's country of origin, we always capitalise the first letter. The countries are proper nouns.
(1) Je viens d'Allemagne
(2) Elle vient d'Irlande
However, when speaking about a person's nationality, do not capitalise the first letter. This is because the nationalities act as adjectives.
(3) Je suis français
(4) Elle est anglaise
The only circumstance in which a person's nationality can be capitalised, is if the nationality is used as a proper noun such as:
(5) C'est un Français qui me l'a dit
(6) Les Chinois qui habitent là sont très sympas
Thus, in written French we continue to capitalise proper nouns when referring to countries. Whereas, with nationalities, we maintain the lower case when describing a person's nationality unless we use the nationality as a proper noun to replace the subject pronoun.