The NFL has announced that it has "no plans to move the start of the league year." (Adam Schefter on Twitter)
There were reportedly meetings being held to discuss closing team facilities given the current pandemic. However, the NFL apparently has no plans on delaying the start of the new year. This would indicate that free agency will start as planned. It still remains to be seen if this will be the case and if there will be further impact, including to the 2020 NFL Draft.