If neither England or France win it but e.g. Germany with Nagelsmann does, I think that this tournament will show that having a good coach is paramount. And 'Goodness' can be measured as employability in a good football league. I'm not convinced that Deschamps or Southgate have many options as club manager.
Maybe Brazil is right that getting Ancelotti as national coach is critical.
Club coaches don't necessarily make good national coaches. Nagelsmann had to eat humble pie quickly and dumb down his tactical ideas to a level that was actually workable within the frame-work of the German NT.
Deschamps reminds me of Löw, who only needed to be smart enough to get out of his players' way out once to win a World Cup. Southgate hasn't shown that ability yet. These first two games this Euro in particular he set up his players almost deliberately so they can't do what they're good at - He's like the antithesis to Carlos Ancelotti.