I've listened to the audio interview. What the deputy says is this: given that Canada refuses to reach an agreement with France regarding an extension of SPM's continental shelf (all the countries in the world bordering a continental shelf have now the right to extend their EEZ from previously 200 nautical miles to now 350 miles, provided they file a dossier at the UN), she said the French government would file a separate dossier to claim the plain orange zone on the map above, and Canada would file a separate dossier to claim the entire area.
The rule at the UN is if two states claim the same continental shelf extension, none of them can exploit it, so the deputy says the French dossier will basically block any possible exploitation of the continental shelf extension by Canada, and so Canada will finally have to sit around the table and negotiate with France (so she hopes).
Asked whether Paris would this time really defend SPM, she said that authorities in Paris have now realized the potential of their overseas maritime areas, in particular off SPM, so there is more understanding of these issues in Paris now than in the 1980s.
She said 60 deputies in the French National Assembly (slightly more than 10% of the National Assembly) have formed a "North America Group" in charge of defending French rights in North America (that's SPM, basically, since we have no other territories anymore in North America
) and pressuring the French government (it will be a legislative lobby pressuring the French executive, in particular pressuring the French foreign office, from what I understand).
She said the #1 aim of this continental shelf extension is not cod fishing (SPM seems to have completely given up on this), but oil. She said the technologies need to be improved for the exploitation of this very deep oil (bottom of the ocean in the orange zone is 3,000 meters below sea-level).
Finally she said more exploration must be done on the continental shelf (claimed by SPM), to assess what riches really lie there. She said only 5% of it is currently known.