French national financial prosecutors said a case had been opened in response to media reports questioning the award by the International Association of Athletics Federations (IAAF), which has been shaken in recent months by a wider corruption and doping scandal.
Coe, who was vice president of IAAF when the games were awarded in April, told BBC Radio Four it was not unprecedented for decisions to be made without a bidding process. Japan's Osaka was given the 2007 event in such circumstances.
"Eugene was not put forward by the IAAF but by US Track and Field," Coe said. "The Council decided this was the best opportunity in the foreseeable future to get the championships into the U.S.
"We did not have cities like Miami or Chicago falling over themselves to put themselves forward."
Eugene is closely linked to U.S. sportswear firm Nike. That connection also caused disquiet as Coe was a long-standing paid ambassador for the company and had to defend himself against accusations that leaked internal Nike emails suggested he supported their bid.
The double Olympic champion denied there was any conflict of interest, but severed the link two weeks ago, describing "noise" around the situation as a distraction as he sought to deal with the doping and corruption crisis.
The French Ministry of Justice issued a statement on Thursday explaining why it had opened the case having been made aware of the unusual nature of the decision and Coe's potential conflict of interest by international media.
"The object is to determine the conditions under which the hosting decision was taken and whether corruption offences, money laundering or a conspiracy to benefit from criminal association have been committed in France."
SPORTING SCANDALS
That broader IAAF scandal mirrors in part a corruption affair shaking world football's governing body, FIFA. Decisions to award the World Cup to Russia and Qatar in 2018 and 2022 have been under investigation, though both countries deny wrongdoing.
Coe's predecessor as president, Lamine Diack, is being questioned by French police over accusations he took payments of hundreds of thousands of dollars to ensure athletes who had failed drugs tests would be free to continue to compete.
The World Anti-Doping Agency WADA has suspended Russia's anti-doping body as part of a crackdown on drug cheating in Russia which has already been suspended from international athletics.
The world championships, which began in 1983 and are now staged every two years, have never been held in the United States, the sport's most powerful nation in terms of performance but which struggles to attract viewers and sponsors.
Coe has previously said that the decision for Eugene was made after a presentation by Diack, who said financial and commercial opportunities had arisen that he felt meant the city should be awarded the rights without contest.
The IAAF Council voted 23-1 in favour, with one abstention, with those behind a potential bid by the Swedish city of Gothenburg left frustrated and confused at the change of tack.
Bjorn Eriksson, leader of the Gothenburg bid and former head of Interpol subsequently said the decision "smelled" and needed an investigation.
Asked about corruption within the organisation on Thursday, Coe said: "If that has happened it would be abhorrent," but said he could not comment further because of police involvement.
"It's a criminal investigation looking at a handful of people, though that's not a comfort for me," he said.
Organisers of the Eugene event said they had done nothing wrong.
"We are very proud of, and we stand by our bid," TrackTown USA President Vin Lananna said on Wednesday. "We stand by the integrity of the bid. We are 100 percent confident there has been nothing outside of what are the norms for the presentation of an IAAF bid."
Eugene lost out to Doha for the 2019 event while the next edition, in 2017, is in London.
(Editing by Ralph Boulton)
