With Barnier ousted the President needs a quick replacement in a difficult impasse.
No budget will mean the 2024 one will rollover increasing the debt level frowned on by Brussels. It is on target for 6 per cent, double the EU guidelines.There will be protests, strikes but unlike US cap no goverment shutdown

Glucksman, Cazenove, Bayrou other mooted centrists look unlikely to garner more support unless Glucksman can split the leftist bloc.
No new parliamentary elections can happen til June for Parliament divided into 3 blocks at present left right and centre.

After Trumps weekend visit for reopening of fire damaged Notre Dame cathedral Macron has very little time or options while both left and right call for him to go.

IMHO and friends close to Bruno Le Maire he may try ride it out Italian style with technocrats. The uncertainty combined with German elections, Trumps tariff and no end to payments to Ukraine makes for an impasse.

It is not impossbile Barnier could return as PM in July but I think he'd do well see if Le Pen is barred and confront her no 2 Jordan Bardella and Melenchon of the left and right to become President once Macron's gone.Bayrou while decent democrat is past it having failed 3 times.

Entre le marteau et L'encume, on verra 'l'avenir inconnu.

Twixt the hammer and the anvil we'll see what the future holds.

More here in English

Marine Le Pen's trap is closing