However, if those teams don't move to the AFC, my guess is that the Saints, Vikings, and Falcons go to the AFC (with the Cardinals being a Wild Card in this process).
One possible present-day alignment for this scenario:
AFC:
East: Baltimore Ravens, Buffalo Bills, New England Patriots, New York Jets
North: Cincinnati Bengals, Indianapolis Colts, Kansas City Chiefs, Minnesota Vikings
South: New Orleans Saints, Miami Dolphins, Jacksonville Jaguars, Atlanta Falcons
West: Denver Broncos, Houston Oilers, Los Angeles Chargers, Las Vegas Raiders
NFC:
East: Philadelphia Eagles, New York Giants, Washington, Pittsburgh Steelers
North: Chicago Bears, Cleveland Browns, Green Bay Packers, Detroit Lions
South: Carolina Panthers, Dallas Cowboys, Tampa Bay Buccaneers, Tennessee Titans
West: San Francisco 49ers, Seattle Seahawks, Arizona Cardinals, Los Angeles Rams
My headcanon for this is that expansion pretty much stays the same until 2002, when the Tennessee Titans begin play as an expansion team (ITTL, the Oilers were successful enough to stay in Houston) in the NFC (so they can have a division rivalry with the Panthers), and the Colts move to the AFC.