France is pitching what it says is a new model of partnership with African countries at a summit that begins Monday in Kenya as it completes a military withdrawal from West African countries that has been widely seen as marking declining influence on the continent.

But Paris is expected to use the two-day Africa Forward Summit, which it is co-hosting, to push a new Africa policy that focuses more on English-speaking countries and offers what it calls a “partnership of equals." Its new defense agreement with Kenya marks the direction it hopes to go.

France has long maintained a policy of economic, political and military sway over its former colonies dubbed Françafrique, which included keeping thousands of troops in the region.…