Final answer:
The British focused on economic dominance followed by direct control through strategic alliances and military power in Asia, exemplified by their victory at the Battle of Plassey. The French, on the other hand, were more reliant on military force and 'barbarian tactics' to maintain control, as seen in their later conquests in North Africa.
Step-by-step explanation:
The French and British had different tactics for controlling their empires in Asia. The British, with their powerful East India Company, initially focused on economic dominance and later asserted more direct control, as seen in their victory at the Battle of Plassey in 1757 against the ruler of Bengal and French allies. This battle signified the British becoming the main power broker in India, leveraging both economic incentives and military power to make allies among local Indian princes.
In contrast, the French, who began their colonial conquest in Asia slightly later, utilized more militaristic and aggressive tactics. After their defeat in the Seven Years' War and the loss of Pondicherry, the French influence in India significantly declined. Later in North Africa, they employed what were described as 'barbarian tactics' to overcome fierce resistance, displaying their reliance on military force to maintain and expand their colonies.
Thus, while both the French and British used a combination of military and economic power to control their territories, the British more strategically developed economic relationships coupled with military power, while the French tended to rely more on military force as a primary means of control.