On Thursday the European Commission told Eurotunnel, which operates the undersea tunnel between France and England, to cut its charges for passenger and freight trains using the route.
The Commission argued that the charges were too high and were discouraging the development of rail traffic and particularly the movement of freight.
Analysts said that this pressure, if realised, would weigh on the company's profits.
The price of shares in Eurotunnel fell by 12.27 percent on Thursday and by 6.46 percent on Friday to 5.13 euros on the Paris stock market.
Eurotunnel chief executive Jacques Gounon announced that the company would ask for an investigation, in a letter to shareholders and published on the company's website.
He said that "five hundred million euros ($656 million) of value was destroyed in two days after the publication last Thursday during stock market trading hours of a press statement by the European Commission concerning, among other things, tariffs for the Channel tunnel."
Gounon said that press reports about this had been published "even before the statement was made".
The company would therefore ask market authorities in France and Britain, where the company is also listed, to check that privileged information published in the press and on social networks "even before the European Commission's statement was published" did not involve "breaches of stock market law."
Gounon objected that the reports had been published before Eurotunnel was aware of the Commission's statement.
The Commission also ruled that Eurotunnel had to end an arrangement whereby it allocated opportunities to use the tunnel to certain rail companies, in France the SNCF, for 65 years.
The two countries now have two months in which two respond to the Commission's ruling. If they do not do so, the Commission may then seize the EU Court of Justice which has the power to impose financial penalties.
Eurotunnel's move is based on a requirement, particularly on the London stock market, that certain types of regulatory information be made available equitably to a wide audience, and usually outside trading hours.
The improper use of such privileged and regulatory information can constitute an offence of insider trading.