Fiat Chrysler Automobiles NV proposed a roughly $40 billion merger with French rival Renault SA, a deal that if completed would create the third-largest auto maker by production and scramble an industry that has been seeking scale to cope with fast-globalizing markets and rapidly changing technology.

If Renault and Fiat Chrysler consummate a deal, it would create a car company with annual vehicle production of almost nine million passenger cars and light trucks. Such a combination would rank behind just Volkswagen AG and Toyota...