Captions are short descriptions that provide some information about pictures, graphs or charts in medium such as books, research articles, websites, magazines and newspapers. For example, in the website: https://fastjapan.com/en/p108335
, there is a caption under each picture of a legendary Japanese athlete to provide more information beyond what the picture is showing (e.g. what the person or people are doing when the shot was taken, brief description of the person's achievements). They are usually found under the pictures, charts and graphs.
On the other hand, subtitles are words found at the bottom of a film or TV program to show what is being said. For example, an English movie can have Japanese subtitles for Japanese viewers who may have problems understanding spoken English even though they may be proficient in written English. Another example would be the videos found in the website: https://www.ted.com/talks
where you are spoilt for choice from a variety of subtitles (e.g. Japanese, Korean, Spanish).
On a separate note, you may have noticed an abbreviation (CC) at the bottom right corner of many Youtube video clips. CC stands for closed captions which actually means subtitles to provide help for people who have hearing difficulties. Close captioning is also used to enhance educational videos, making them more beneficial for students in terms of their learning of pronunciation, reading and listening skills.
As you can see, "captions" and "subtitles" can mean the same thing nowadays in both your sentences. You can choose French "captions" or "subtitles" for an English video. You can also choose English "caption" though you are a native English speaker. However, when you read a description of a picture in an article, you are reading the "captions", not "subtitles".
I hope this helps.