It's this one Paris 2024 signed, called "La Charte d’Engagement LGBT+" in French, which is much closer to the English translation you quoted ("LBGT+ Commitment"):
BTW, the EC might not list that one, but French government does. (Apparently said charter was also signed [in Jan 2013] by [former] minister of social affairs and healthcare Marisol Touraine, when she was in office, during the Socialist government.)
Finally, the Diversity Charters that EC lists in that particular directory (that you've linked in the Q) have a much broader scope than LGBT, judging by the French one you've linked to. The articles of that one don't even mention LGBT as such, by the way, but something like:
Favoriser la représentation de la diversité de la société française dans toutes ses différences et ses richesses, les composantes culturelle, ethnique et sociale, au sein des effectifs et à tous les niveaux de responsabilité.
Google translation:
Promote the representation of the diversity of French society in all its differences and riches, the cultural, ethnic and social components, within the workforce and at all levels of responsibility.
So, I can see how LGBT+ rights' advocates would prefer that organizations sign something more specific in that respect. (BTW, the "Charte d’Engagement LGBT+" was launched about 9 years later than the Diversity Charter; 2013 vs 2004.)