While I won't argue that US election campaigns are long, the counting afterwards has a good explanation. The two big factors that make counting votes so complex is we have 50 versions of elections, and we bote for everything at once.

I've heard that French presidential campaigns take like one night but if I recall correctly the only thing being voted on is the presidential candidate. This makes hand sifting of the ballot into piles extremely easy and then a machine or person can just count them.

In the US you vote for a whole slew of things all at once. Proposed changes to state law through propositions, your house representative, your governor, you STATE representative, senator, STATE senator, sheriff, university head, city council, and on and on and on. So tabulating all these is a bit more complicated.

Then you have the 50 different systems. So Mississippi is going to take a while, that's because they allow for absentee mail in ballots to come in 5 days late and if a voter on election day didn't have proper ID they have 5 days to shoe proper ID and then vote. This guarantees it is going to take long after voting day to get results.