When did France become a republic?
France
In August 1791, the Emperor of Austria and the King of Prussia in the Declaration of Pillnitz threatened revolutionary France to intervene by force of arms to restore the French absolute monarchy. In September 1791, the National Constituent Assembly forced King Louis XVI to accept the French Constitution of 1791, thus turning the French absolute monarchy into a constitutional monarchy. In the newly established Legislative Assembly (October 1791), enmity developed and deepened between a group, later called the 'Girondins', who favored war with Austria and Prussia, and a group later called 'Montagnards' or 'Jacobins', who opposed such a war. A majority in the Assembly in 1792 however saw a war with Austria and Prussia as a chance to boost the popularity of the revolutionary government, and thought that France would win a war against those gathered monarchies. On 20 April 1792, therefore, they declared war on Austria.
On 10 August 1792, an angry crowd threatened the palace of King Louis XVI, who took refuge in the Legislative Assembly.
A Prussian army invaded France later in August 1792.
In early September, Parisians, infuriated by the Prussian army capturing Verdun and counter-revolutionary uprisings in the west of France, murdered between 1,000 and 1,500 prisoners by raiding the Parisian prisons. The Assembly and the Paris city council seemed unable to stop that bloodshed. The National Convention, chosen in the first elections under male universal suffrage, on 20 September 1792 succeeded the Legislative Assembly and on 21 September abolished the monarchy by proclaiming the French First Republic.
Ex-King Louis XVI was convicted of treason and guillotined in January 1793.
France had declared war on England and the Dutch Republic in November 1792 and did the same on Spain in March 1793; in the spring of 1793, Austria, Great Britain and the Dutch Republic invaded France; in March, France created a "sister republic" in the "Republic of Mainz".
Republic
The French Revolution was also not republican at its outset. Only after the Flight to Varennes removed most of the remaining sympathy for the king was a republic declared and Louis XVI sent to the guillotine. The stunning success of France in the French Revolutionary Wars saw republics spread by force of arms across much of Europe as a series of client republics were set up across the continent. The rise of Napoleon saw the end of the French First Republic and her Sister Republics, each replaced by "popular monarchies". Throughout the Napoleonic period, the victors extinguished many of the oldest republics on the continent, including the Republic of Venice, the Republic of Genoa, and the Dutch Republic. They were eventually transformed into monarchies or absorbed into neighbouring monarchies.