I dont cry much with music. But I just watched this for the first time and I almost did. I dont even like the french language. The next bit is from a comment on the video to give a bit of context.

For those saying she lost a loved one, or got divorced...none of this is true.

Lara was simply coming out of a really rough time mentally because of both her professional life and her personal life. She had had suicidal thoughts, to sum it up. She explained it several times during interviews.
Her pianist and a fan arranged this moment, and the entire audience sang for her, changing the words to “On t’aime” which means “we love you”. Lara said during this moment, she realized the beauty of life, and that it’s really worth living it.