Final answer:
The British and French competed intensely in North America, vying for control over various territories during colonial wars like Queen Anne's War and King George's War.
Step-by-step explanation:
The region where the British intensely competed with the French was North America. This competition was particularly evident during various colonial wars, such as Queen Anne's War and King George's War, where control over different territories like Acadia and other parts of North America was contested. These conflicts were part of the broader struggle for colonial dominance between the two European powers.