The pair didn't reveal details in comments to reporters after the meeting, but did indicate the session was "positive" and "productive."
Both drivers served as pallbearers for Wheldon during his funeral service Saturday in St. Petersburg, Fla.
"We all got to talk a lot and listen a lot," four-time series champion Franchitti said. "We just looked at going forward and how do we improve things in all areas, so I think it was a very positive and productive meeting. That's the first step I think today."
IndyCar also officially launched a two-phase investigation into the horrific Oct. 16 crash in Las Vegas, which involved 15 cars and claimed the life of Wheldon, a two-time Indianapolis 500 winner.
The first phase will include a safety and competition evaluation to arrive at a definitive explanation of what caused the accident, while Phase 2 will use the information to minimize future risks.