His army is one of the best trained and equipped in the semi-arid belt of Africa known as the Sahel, and it has played host to military exercises conducted by the United States.

In an email, Col. Christopher Karns, a spokesman for the Pentagon’s Africa Command, said Chad was a major partner in an effort involving several countries in the Lake Chad basin to fight Boko Haram.

France, for its part, did its utmost to protect Mr. Déby himself, deploying troops to Chad in 2008 and 2019 to defeat rebels who tried to unseat him.

After three decades in power, Mr. Déby was aiming for a fourth. In 2018, Chad’s parliament revised the Constitution to allow him to stay in office until 2033. Analysts say his sudden death will likely throw Chad’s politics into disarray.

Some were skeptical that his son Mahamat could hold on for long in the face of challenges from rivals in the security establishment or disaffected members of his own Zaghawa ethnic group, where some had bristled at the rise of Mr. Déby’s family.

“The prospects of more splits within the military is significant,” said Judd Devermont, director of the Africa program at the Center for Strategic and International Studies in Washington. Others speculated that France would struggle to find a new partner in a country that French leaders long considered their African backyard.

“The French have been so associated with Déby — not just propping him up but also eliminating his enemies on his behalf — that they will have a hard time establishing any credibility with a successor regime that doesn’t have the last name Déby and isn’t a Zaghawa,” said Cameron Hudson, an Africa expert at the Atlantic Council.

Eric Schmitt contributed reporting from Washington.

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