What if the US adopted a semi-presidential system a la France?

Title. What if instead of the presidential system we currently have in place, the US adopted a semi-presidential system a la modern-day France.

For further context, pretty much acting like this:
"In France, for example, in case of cohabitation, when the president and the prime minister come from opposing parties, the president oversees foreign policy and defence policy (these are generally called les prérogatives présidentielles (the presidential prerogatives) and the prime minister domestic policy and economic policy.[12] In this case, the division of responsibilities between the prime minister and the president is not explicitly stated in the constitution, but has evolved as a political convention based on the constitutional principle that the prime minister is appointed (with the subsequent approval of a parliament majority) and dismissed by the president.[13] On the other hand, whenever the president is from the same party as the prime minister who leads the conseil de gouvernement (cabinet), he/she often (if not usually) exercises de facto control over all fields of policy via the prime minister. It is up to the president to decide how much "autonomy" is left to "their" prime minister to act on their own."
(https://en.wikipedia.org/wiki/Semi-presidential_system)
 
Do you mean the France of 1958-2002 or post-2002?

Since the referendum that shortened the presidential term to five years (same length as a parliamentary term), France is basically a presidential republic now. The voters have elected the same party for both the presidency and the Assemblée nationale each time.
 
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