The Decree concerning the requirements on labeling mandatory indications was published on August 21st, 2016 and it deals with prepacked food -manufactured and marketed in France (intended for final consumers) only- while it does not consider prepacked food manufactured in other countries (EU Member States or other States) and PGI products. 
The products concerned are marketed milk, dairy products (yogurts, butter, cheese…) with milk as ingredient and processed food with meat (beef, pork, sheep, goats, poultry) used as ingredient.
As for meat, the country of birth, rearing and slaughter of animals has to be stated and to do this, some formulas are available depending on whether the meat has a single country of origin or more countries (“EU origin”, “non-EU origin”). As for milk, the country of collection, packaging or processing has to be specified. This information has to be stated in the list of ingredients just after the relevant ingredient or with a note at the end of the list. 
Order of September 28th, 2016 implementing Decree no. 2016-1137 relating to the indication of the origin of milk, milk and meat as ingredient (published on September 30th, 2016). The article 1.I.3 of Decree lists two thresholds for dairy products and processed products.
A transitional period after the entry into force of this new rule is envisaged and food products which do not comply with these new requirements can be sold until March 31, 2017. Product traceability will last for five years and some financial penalties are envisaged in case of non-compliance with the provisions.

Source: Legifrance