John, you’ve asked me before about Ségolène Royal, on April 5th to be precise, here (I’m going to start thinking you fancy her!).
I’ll spare you the bother of reading my spiel if you’ve forgotten what I wrote, the answer to your Q is: very unlikely. And even if she fancied it she’d never make the primaries (another pb is that she left the Socialist party a few years ago so she’d have a job being accepted in the primaries, although it’s technically possible), as I wrote then she could go it alone but as an independent candidate, forget it, she’d struggle to get even 2-3% and therefore could lose a lot of money, although I’m sure she’d be smart enough to get others to fork out for her campaign (below 5%, the state doesn’t reimburse the campaign expenses, which is nearly what happened to the Parti Socialiste last time in 2017 as they only recorded 6.4%! Phew…).
Royal has got other plans, she’s currently after what’s known as a “pantouflerie” – a well-paid sinecure – and as such has set her heart on being elected as a Sénatrice representing French citizens overseas, which as sinecures go that one probably tops the cushy league, along with MEP.
Sénat : Ségolène Royal candidate pour les Français de l’étranger
The approx. 3 million – registered – French citizens abroad are represented by 23 MPs, 12 sénateurs/trices and 11 député.e.s. This election (originally due in Sept. 2020 but postponed because of the pandemic) to elect 6 of them will be held in September 2021. As you may know, senators are indirectly elected, by what’s called “grands électeurs”, see this wiki.