FEMA Assistance Relief Act of 2020 This bill modifies the federal cost share of certain emergency assistance relating to COVID-19 (i.e., coronavirus disease 2019). Specifically, the bill provides for (1) a 100% federal cost share of assistance provided under the emergency declaration issued by the President on March 13, 2020, relating to COVID-19 and any subsequent major disaster declaration that supersedes it; and (2) at least a 90% federal cost share of assistance provided for any emergency or major disaster declared by the President from January 1-December 31, 2020. With respect to the emergency declaration issued on March 13, 2020, the President may provide assistance for activities, costs, and purchases of states or local governments or the owners or operators of eligible private nonprofits, including, among other things backfill costs for first responders and other essential employees who are ill or quarantined; increased operating costs for essential government services due to such emergency; costs associated with maintaining alternate care facilities or related facilities currently inactive but related to future needs tied to the ongoing pandemic event; personal protective equipment and other critical supplies and services for first responders and other essential employees; and costs of procuring and distributing food to individuals affected by the pandemic through networks established by state, local, or tribal governments or other organizations.