TOKYO — It was a simple plan. Renault and Nissan, two partners in a vast auto-making alliance, would pool their resources to build a new low-cost car in, and for, emerging markets.

Each company, working from a factory near Chennai, India, would add its own branding and finishes, but the platform — the vehicles’ bones — would be the same. Carlos Ghosn, the alliance’s chief executive, believed that shared engineering was necessary for the French and Japanese companies to prosper in an increasingly competitive industry.

But the two teams — despite both being led by French engineers — could not agree on a design, people familiar with the matter said. When Nissan’s cars hit the market in 2014 and Renault’s in 2015, they were different, even at the chassis. Mr. Ghosn was frustrated and disappointed, one of the people said, and saw the companies as ignoring his direct instructions.

Today, Mr. Ghosn sits in a Tokyo jail. And the two executives now at the top of the alliance must figure out how to overcome the fierce corporate pride that has fueled Renault and Nissan’s past rivalry and secure the companies’ successful cooperation.