Final answer:
The most influential circumstance in provoking the French and Indian War was the push for control over the Ohio River Valley, claimed by both British and French colonial interests. Virginian expansion into the area and subsequent French military response set the stage for the outbreak of the war. This territory struggle is viewed as the key factor leading to the broader conflict.
Step-by-step explanation:
The circumstance that was most influential in provoking the French and Indian War was the colonial expansion and competition for territory in the Ohio River Valley. This tension escalated when Virginians, including a young militia leader George Washington, crossed into the region, thereby contesting the area claimed by both French and British interests. The French responded by building forts in western Pennsylvania, triggering a series of events that culminated in open conflict.
The intense rivalry over the Ohio Valley, an area of strategic importance for trade and territorial control, led to the war which is also globally recognized as the Seven Years' War. Control of this region would determine the fate of North American colonial possessions and, therefore, was the spark that ignited the wider conflict. The eventual British victory and removal of French power from North America had significant consequences, leading to Pontiac's War with Native American tribes and contributing to the changing British policies that ultimately fostered colonial discontent.
Moreover, the war emphasized the existing sense of autonomy among the colonies, setting the stage for future debates over states' rights and federal power in the early United States. The conflict also had global implications, changing the balance of power between European nations and reshaping international affairs.