Relaunching America's Workforce Act This bill establishes several grant programs to address employment, the workforce, and education access in response to the COVID-19 national emergency. The Department of Labor must provide grants in response to the COVID-19 national emergency to provide training and employment for dislocated, unemployed, and underemployed workers; support youth employment; establish workforce information systems improvements; provide reentry employment opportunities for justice-involved youth and young adults; and create or expand apprenticeship programs. Programs directed towards assisting Native Americans and migrant and seasonal farmworkers may be extended. The Department of Education must provide grants to expand the capacity of adult education providers to prioritize serving adults with low-literacy or numeracy levels negatively impacted by the COVID-19 national emergency, and to improve or expand career and technical education programs and programs of study to respond to state and local needs as a result of the COVID-19 national emergency.