The first French Republican War broke out in 1768 when after the death of the more cool-headed kings Humphrey III and IV of Britain and Héctor II of Spain, who had been self-assured enough not to be impressed by the king-less situation of France, diplomatic tensions to France rapidly worsened. Savoy, the Netherlands, even Hungary under hesitating Charles VI and many German states joined the coalition; only Italy stayed neutral.
1768, September: Battle of Verdun. German armies defeat French.
1769: France orders the "levee en masse", creating the republican armies.
The pope flees from Avignon, first down the Rhone river to Corse, but later moves his seat to Toledo, Spain, since Italy still doesn't want to enter the war. In Spain, he outspeaks decidedly against republicanism, further encouraging the "monarchist crusade" feeling among the reigning classes in Europe. There are some hopes among conservatives that this may bring the national churches closer together and give the pope more power.
1769, April: British troops land in Aquitaine, to unite with the Spaniards.
1769, May: Battle of Aix-en-Provence - "the blackest day for the house of Savoy": Crown prince Filiberto is captured by the French, his brother Filippo and their cousin (also named Filippo) die in battle.
1769, August: Battle of Belfort. French kick out German troops from French soil. However, the Swiss Confederation now enters the war against France.
1770, March: Battle of De Panne. French defeat Dutch, who complain that the Brits didn't support them.
1770, July: British-Spanish army defeated before Limoges. Spain retreats from France, fights defensively.
1770, September: Battle of Pont-a-Mousson. German-Swiss-Hungarian troops defeated by French.
1771, February: Spaniards fight off French attack against the Pyrenees.
1771, July: Battle of Saarbrücken. French occupy SW Germany between Mosel and Rhine rivers.
1771, November: French Royalists in Algeria attempt a landing, supported by the Spanish navy, in South France. The landing itself is successful, but the people don't rise against the republic, and the landed troops are defeated. Many ships have to be abandoned.
1772, January: After the French used the holidays to move their armies, while the Spaniards were celebrating, Catalonia is overrun by the French.
1772, April: Battle of Maasmechelen. Last German-Dutch army defeated.
In the Peace of Brussels 1772, all the German lands west of the Rhine were annexed by France, plus the lands of Berg and Baden at the right bank. So were Spain north of the Ebro, French-speaking Switzerland, the Alsace, (old) Savoy and Nice. Switzerland was neutralized again.
The monarchs weren't exactly happy how the war had turned out and hoped that France would show a weakness, so they'd have a chance to re-attack.