LONDON--French competition authorities are investigating delivery companies Royal Mail PLC, TNT Express NV and FedEx Corp. over allegations they breached antitrust laws in the parcel market, which could lead to material fines.

Royal Mail, the recently-privatized U.K. postal operator, and TNT Express, of the Netherlands, both confirmed the probe Wednesday, while U.S.-based FedEx disclosed the investigation on Monday. All three companies warned that the investigation could result in a material loss.

A spokesman for the French competition authority, the Authorité de la Concurrence, confirmed the agency was undertaking a probe into parcel delivery services but declined to identify the companies or the practices being examined.

At 10:04 GMT shares in Royal Mail traded down 0.4%, while TNT Express dropped 2.4%.

Royal Mail said the allegations related to its GLS France subsidiary, adding that it was too early to "determine the amount or range of potential loss, however, it is possible that it could be material."

TNT said "it cannot be excluded that TNT Express will be fined for a material amount as a result of this procedure," adding that it had been cooperating with the French competition authority since it began its investigation in 2010.

In a regulatory filing Monday, FedEx said the probe related to alleged actions at trade-association meetings of former general managers at its Tatex division, before the company bought the business in 2012.

FedEx said it was too early to calculate the potential loss, but said "it is reasonably possible that it could be material."

Analysts at Espirito Santo said the impact of the probe could be worse for TNT than for Royal Mail because GLS--the Royal Mail unit under investigation--has just a 5.6% share of the French market, compared with TNT's 19.6% share.

William Horobin and Maria Armental contributed to this article.

Write to Ed Ballard at ed.ballard@wsj.com

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