The overseas war were a bit more than the "French and Indian" War. India was also up for grabs. If France could control the far east trade it's power would be cemented for a while after.
Struggle for Empire? What are you speaking of, Europe? If so domination was still his goal, his latter wars were to make France's position invulnerable, but not to conquer all of western Europe.
France had not been for "centuries" the premier military power, for perhaps a century or less. The Seven Years war really showed what dire straights the French Army was in.
Bookmarks