The French are as dumb as the Brits. Both countries executed their monarchs to be instantly gratified, creating more problems for themselves in the long-run, only to once again return to a monarchy. France’s last monarchy ran from 1852 to 1870. After Lord Protector Oliver Cromwell died in 1658, his son decided he didn’t want to succeed his father, so the Brits begged Charles II to return to England from exile, so the monarchy could be restored.
Thats one effect. There were others. Which is why I highly recommend Paul Johnsons “Birth of the Modern”. Napoleons influence reached from Portugal to Russia. He turned everything in Europe upside down. The independence of Brazil to the Decembrist plot, just to name a couple, were all inspired to a degree by his actions and memory.
Complex business.
If you read the Commonwealth Protectorate Constitution - called ‘Instrument of Governance’ later revised and called ‘Petition and Advice’ they sound surprisingly modern. They will also seem very familiar! They were the first examples of a written constitution for a nation.