“We can’t intervene just because there might be a negative impact for companies in the ecosystem,” said

Isabelle de Silva,

head of France’s competition authority, at a press conference. “At this stage, we haven’t found flagrant examples of discrimination.”

The authority said, however, that it plans to pursue an in-depth investigation to determine whether Apple’s changes could be regarded as “self-preferencing” by imposing stricter rules on third-party apps than it does on itself. That investigation could stretch to next year, Ms. de Silva said.

Wednesday’s decision removes one source of doubt over Apple’s plans, announced last year, to require apps on its smartphones and tablets to get opt-in permission from users before collecting their advertising identifiers, unique strings of letters and numbers that companies use to identify individuals in order to show them targeted ads and monitor how ad campaigns performed.

Privacy advocates and regulators have generally praised moves like Apple’s, saying consumers should have as much control as possible over how their data is collected and used. In recent years, a push toward greater online privacy has resulted in new laws in Europe and California. But companies in the online-advertising ecosystem have said such changes put them at a competitive disadvantage.

The companies behind the complaint, filed last fall through a group of trade associations, had argued few Apple users will agree to be tracked, making it harder for apps to make money from personalized ads and hurting companies that broker their sale.

Damien Geradin, the competition lawyer representing the coalition of industry groups, said the companies were disappointed with the French decision but satisfied that the authority would pursue an in-depth investigation. “Apple is not off the hook yet,” Mr. Geradin said.

Apple applauded the decision and said it would work with the authority on its investigation. “We firmly believe that users’ data belongs to them, and that they should control when that data is shared, and with whom,” an Apple spokesman said.

The French regulator’s decision comes as tech giants including Apple,

Alphabet Inc.’s

Google,

Amazon.com Inc.

and

Facebook Inc.

are coming under growing scrutiny in Europe and the U.S.—both on antitrust grounds for their treatment of smaller rivals, and on privacy grounds, for their collection of users personal information.

Wednesday’s decision is the first major one to highlight how that push to protecting user privacy can be at odds with regulators’ efforts to safeguard online competition. That is because one of tech’s most popular business models is targeting advertising at individuals based on their online behavior, and smaller companies sometimes accuse the giants of using privacy as a pretext to cut off data they need to do so.

Earlier this month, some companies complained that Google’s plan to stop supporting or using technology that tracks individuals’ web browsing behavior for advertising purposes would simply increase Google’s ad monopoly because it already has so much data about users from its own properties.

“We are seeing more and more competition questions around privacy and data protection,” Ms. de Silva said Wednesday, adding that she had solicited advice from France’s privacy regulator, which she said had backed Apple’s plans as good for users and neutrally applied.

Ms. de Silva said her authority might also investigate Google’s plan to remove tracking technology from its Chrome browser, similarly to the U.K.’s Competition and Markets Authority.

Facebook has also attacked the Apple plan, arguing that it is an abuse of dominance that would hurt smaller companies. But restricting Apple’s identifiers would also undermine one strength of Facebook’s business: how it gathers data from mobile apps on what people do on the apps, what they search for, what they buy and more.

The complaint that led to Wednesday’s decision centers on Apple’s move to introduce its own language asking users to opt in, separate from the prompts already required by European privacy law.

The complaint also highlighted how Apple was still able to gather data about iPhone users through their use of Apple apps, giving the Cupertino, Calif., company an unfair advantage over other apps when it sells targeted ads in its own App Store. It is on this latter point that the authority said it would continue to investigate.

In her press conference, Ms. de Silva said that dominant companies have the right to set rules for their services, so long as those rules aren’t anticompetitive or applied unfairly.

“We will be very vigilant,” Ms. de Silva said.

Write to Sam Schechner at sam.schechner@wsj.com