Members of the European Parliament are to ask the French government to clarify whether the European Parliament's buildings on French territory, in Strasbourg, will be subject to surveillance operations under this law.
The MEPs are concerned that they can now be snooped on when they hold their meetings in the parliament building in Strasbourg, which is the capital city of the Alsace region in northeastern France.
They will also demand the European Commission investigates whether the new law is in line with the EU treaties and the Charter of Fundamental Rights, and will raise concerns about the compatibility of some of the law's provisions with the European treaties with the Commission's director for criminal justice, Francisco Morillo.
The new law, passed by the National Assembly on 23 June and the Senate on 24 June, allows the French authorities to intercept and spy on citizens' communications under the pretext of national security, say MEPs who requested the debate.
However, MEPs are concerned about the extensive scope of grounds allowing for surveillance by intelligence services, the data collection and retention mechanisms, the use of the information (purpose limitation), oversight and the rights of individuals.
The news of the investigations comes in the week that it was revealed that former French President Nicolas Sarkozy secretly gave French special services the authorization to intercept submarine communications between 2008 and 2013.
Meanwhile, in a further twist, WikiLeaks revealed a decade-long policy of economic espionage against France by the US National Security Agency (NSA), including the interception of all French corporate contracts and negotiations valued at more than $200 million.
Any investigation into whether the new surveillance powers could — legally — be use to snoop on MEPs while they are going about their European Union business is likely to cause huge embarrassment to the French Government.