I know the term was first used during the Peninsular War in the 1800s, but there are also so many instances it was used before it had a name.
Guerrilla warfare originates earlier than the 1800s and contemporary military authors called it ' la petit guerre' meaning little war. I am not too familiar with earlier than the late seventeenth century in warfare but I have been told that some instances of guerrilla warfare occurred in later middle ages and renaissance era battles. The practice did appear in the early parts of the eighteenth century and with the development of light infantry or skirmish tactics, it would become an integral part of European armies to use. I define light infantry and skirmish tactics as different than the regular linear tactics that most people associate with the era. I hesitate to equate light infantry tactics with guerrilla warfare but in some cases they do go hand in hand. Skirmish and screening tactics of the light infantry synchronize well with guerrilla tactics.
I've discussed light infantry tactics before from the British perspective, which I'll try to link within. The British faced la petit guerre at least by the French and Indian War in the American colonies, but had established a quasi-light infantry doctrine before then with their experience in the War of Austrian Succession and even the 1745 Jacobite Rising. However, light infantry companies or regiments would not appear until the later 1750s with the need for changes in doctrine after fighting French and Native American forces. While the British army had used some light infantry tactics in the War of Austrian Succession, the commanders would begin to incorporate more of it for the American theatre along with other irregular tactics. Lord Howe and Colonel Thomas Gage implemented irregular doctrines in not only military exercises but the way the soldiers dressed. Hats cut down to a brim of an inch and a half, coats shortened and stripped of lace, wool leggings in the manner of Native Americans and they lightened the load carried by soldiers.
The French origins of La Petite Guerre started in the War of Austrian Succession and would be published in military treatises by the 1750s, establishing it as a normal means of fighting along with linear maneuvers. I've yet to find an English translation freely distributed Armand François de La Croix’s Trait’e de la Petite Guerre pour les Compagnies Franches or Thomas Auguste le Roy de Grandmaison’s La Petite Guerre so I cannot say exactly what their treatises entailed in regards to La Petite Guerre. However, these are some of the earliest published books with the term and its doctrine established from the Austrian war.
Back to the American theaters of war, the colonists, both English and French, had already adapted irregular warfare as their main doctrine of fighting. Contemporaries called it "bush fighting" or "Indian method" of fighting. Attacks on the frontier settlements shaped how local militias and provincial forces would respond and often did not take any shape close to linear warfare. When British soldiers fought in the initial years of the French and Indian War, they used linear tactics with large units to give massive volley fires. These did continue throughout the war but with the establishment of irregular units such as Rogers' Rangers, and the 80th Lightly Armed regiment, irregular would become a bigger part of the battles. British army officers and non commissioned officers would detach from their regiments to learn directly from Robert Rogers and bring back the knowledge to their regiments. I want to point out that two types of Rangers existed in this era: the kind that Robert Rogers established with an irregular unit that could be a company or a corps; the other being a ranging unit created by volunteers of a local militia to act as a frontier scout, who would go on short patrols and often on horse back. I would think of the later as light dragoons than anything else.
The irregular warfare in the colonies would branch off into the bush fighting that further developed during the French and Indian War, but the military leaders did not label this as La Petite Guerre, which may suggest that they thought the two as separate styles. However, similar or different, the term did appear in French texts in the 1750s and become an integral part of warfare for American theatres of conflicts involving large armies. I find it ironic that the British would add it to their repertoire but still call it irregular, even when it became just as frequent in use as linear warfare.
Sources:
Jack Owen, Jr. The Influence of Warfare in Colonial America: On the Development of British Light Infantry.
Roger Stevenson, Military Instructions for Officers Detached in the Field Containing A Scheme For Forming A Corps Of A Partisan (1775).
“Essay on Regular and Irregular Forces,” Gentleman’s Magazine (1746)
Matthew Spring, With Zeal and With Bayonets Only
Stephen Brumwell, Redcoats.