google: the French version of the page does not behave correctly in the indexes

Our home page has two versions:

The first in French, the second in English. Both versions have been online for many weeks.

Searching Google or Bing from your .FR domains does not produce results for the French version of the page. However, making a site: In the English version of Google it returns:

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Meta tags on the French page:

Meta tags in the English page:

My questions are:

  • Have I correctly configured the meta tags?
  • If not, should Google show the alternative version in French in the results in English?
  • Why is the French version shown higher than the English homepage in the previous results?