France declared war on Austria, Holland and England shortly after the French Revolution; other European powers wanted to put down the French Revolution and restore the monarchy to power. These countries saw the revolution as a grave threat to their own monarchies.
The French Revolution caused a massive shift in European politics. After the French monarchy was overthrown, many of France's former enemies looked on with confusion, wondering if their goals would be better served attempting to restore their former enemies to power, or simply taking advantage of the chaos in France to stake their own claims. Austria was the first to move in 1791, with the Holy Roman Emperor Leopold II declaring his intent to protect the royal family of France. France, in turn, declared war on Austria for its refusal to retreat from France's borders.
In the first year of war France took a number of territories, including Sardinia, as well as territory in the Netherlands and Germany. England and Holland, among other European powers, demanded that France give up its conquered territories. France refused, declaring war in retaliation. The conflict lasted almost 10 years, ending in 1802, leading to a temporary peace when the English and French signed the Treaty of Amiens.