Shareholders also fear that the rules will stem investor activism. If activists do not have as much voting power to change boards and companies, their job will become much harder. And they will be unwilling to lock up millions in capital and wait years to earn significant influence.

Following its shareholder clientele, the world’s largest proxy adviser, Institutional Shareholder Services, has issued a note largely opposing these rules. I.S.S. says it will recommend in some cases that shareholders withhold votes for directors of companies that adopt the new voting rule.

For French corporations, the reasons for opposition are even more complicated. Some have wanted this rule simply because they buy into it as part of good corporate governance. Yet many French companies have significant shareholders already, including the biggest of them all, the French government.

With double voting rights, you could end up with stakeholders with divergent interests and different degrees of power. One can easily see how the interests of the French state might not always align with those of other shareholders, particularly when it comes to preserving jobs.

Some French companies have actively resisted. Renault, Orange, Vivendi and others have pushed for votes to allow the companies to opt out.

In some cases, it has resulted in a chess game, as shareholders and companies plot moves and countermoves. For example, the French government bought $1.4 billion worth of shares to block Renault from opting out of the

voting law. Meanwhile, Nissan, the owner of 15 percent of Renault, is fuming, as its shares do not even have voting rights.

Vivendi, too, faced the issue of whether to opt out of the rule in light of the fierce support of the French billionaire Vincent Bolloré, who owns 14.5 percent of Vivendi. Mr. Bolloré vocally pressed for adoption of the new voting rule, a position for which the economy minister, Emmanuel Macron, offered his “full support.” Maybe not so coincidentally, Vivendi has been a target of the hedge fund P. Schoenfeld Asset Management. In a recent vote, Vivendi shareholders chose against opting out.