There is probably never a good time for an auto empire to have its leader thrown in jail. But for Nissan and Renault, the arrest of Carlos Ghosn comes at an especially inopportune moment.

The two carmakers can ill afford turmoil in the alliance headed by Mr. Ghosn when the global auto market is entering a downturn, a trade war provoked by the Trump administration is interfering with supply chains and Silicon Valley is spawning well-financed new competitors.

Mr. Ghosn’s arrest in Tokyo this week on suspicion that he deceived Japanese authorities about his pay package, exposed deep fissures in the union between Renault and Nissan that he engineered in 1999, and which Mitsubishi Motors joined in 2016.

Whatever the outcome of legal proceedings against Mr. Ghosn, he is unlikely to regain his previous stature. Instead, analysts said, there could be a destructive power struggle within the alliance as Nissan tries to assert more control. Renault has been the dominant partner of the three carmakers even though Nissan sells more cars, a state of affairs that appears to rankle executives in Tokyo.