Whatever one thinks of Michel Barnier’s government or Michel Barnier himself, it is necessary, for the dignity of the Institutions (or what remains of them), for his government to fall. Indeed, the function of Prime Minister would be terribly diminished if it were reduced to the rank of collaborator rather than of President (already a major dysfunction initiated by Nicolas Sarkozy), but of a leader of a political party. In this case, Marine Le Pen. This would be the Fourth Republic at its worst.
Michel Barnier is in no way responsible for this situation and he does not have the means to get out of it. The responsibility for the crisis and for any possible way out of it lies with Emmanuel Macron.
President's resignation? Technocrat government until the next dissolution in June 2025? This seems to be the only (rather bleak) prospects for a fifth term in agony. And the logical follow-up to having attempted to govern France without a majority since June 2022.