So while re-reading Susan Nagel's bio Marie-Thérése I came across an interesting passage: basically the Duchesse de Berry badgered her father-in-law to be proclaimed Regent, which he said she would 'when they returned to France' (the Bourbons were in exile after the July Revolution). Then after the Duchesse landed in France to try and raise an uprising, issuing manifestos calling herself Regent of France, Charles angerly responded that she was not the Regent.
So my question is this: legally do abdicated monarchs have any right to actually designate a Regent for an underage monarch and even if they do can they actually strip someone of the Regency? The one way I can think of that Charles would have the power to do so is as Head of the Royal House, but not much else. So would this violate any fundamental law or was regencies to murky?