Why Would the USAF Buy French Mirages?

Because they don't want the planes sold to the Iraqi Air Force, and this would take them off the market, so the Iraqis could buy F-16s:

This is an interesting rumor. While the Mirage F-1 has almost reached the end of the line as an operational asset with the AdA, it remains a capable fighter and should stay in service for about another decade with a few other air forces (Ecuador, Morocco, and Iran). The Iraqis have recently requested that France delivers the 24 pre-embargo F-1s ordered at the time by the regime of Saddam Hussein in 1985. The Iraqi air force has a long, and relatively successful, history with the F-1 and is particularly looking forward to rebuilding its air defense capability with an aircraft it knows well. However, things are somewhat more complicated; there has been a long standing rumor of F-16s going to the Iraqi Air Force instead and lately, it would also appear that the UAE Mirage 2000-9s have entered the fray.

Sorry, but if this is true, and note that it only a rumor, some heads should roll.

While I understand how US Air Force officers might favor the F-16, it is something that they are familiar with, the idea that they would purchase the aircraft in order to clear the way for a defense contractor is over the top.

This appears to be a decision driven by a desire by some Air Force officers to secure a cushy gig at Lockheed-Martin in retirement, not a decision driven by the real needs and capabilities of the Iraqi military.