If the EU won’t consider themselves to be at war when the part of the EU defensive pact zone that is called Greenland is invaded, they’re losing all credibility both internally and externally. Why would the EU defend Finland or the Baltics or Cyprus? Why would the EU organize against foreign powers funding violent rebellions inside EU territory (similar to how Russia funded Transnistria or the US funded the contras in Nicaragua)?
There is no better red line for France to launch their nukes than the invasion of Greenland. As seen with Russia, any grace given to cult of personality dictators only emboldens them and their worshipers. The only fair response to madman theory is to call the ‘insane’ administration’s bluff and let the people who don’t want them and their families to become radioactive piles of ash take the responsibility of defying insane orders.
Nuclear war would actually cool the oceans. All nuclear bombs combined contain about the same energy as Hurricane Katrina or a small supervolcano eruption. There would be a small fraction of a degree of temporary increase in global atmospheric temperatures, quickly overwhelmed by the nuclear winter as ash and dust in the upper atmosphere reduce global temperatures by several degrees for several years.
The only way I see humanity boiling the oceans is by deliberately releasing global-industrial quantities of super-effective greenhouse gases, actively designed to make the Earth as well-insulated as possible.