Francis, the son of a methodist clergyman from Gas City, Indiana, was educated at Allegheny College and Yale where he obtained his MD in 1925. He worked with the Rockefeller Institute from 1925 to 1938 and, after serving as professor and chairman of bacteriology at the New York University College of Medicine, moved to the University of Michigan in 1941 as professor of epidemiology, a post he retained until his death.

Francis became known to a wide public when, in 1954, he reported on the Salk polio vaccine trial. Before this however he had worked for over 20 years on the epidemiology of the influenza virus. The first such virus, the A-type, had been detected by Christopher Andrewes and his colleagues in 1933. In the following year Francis found a further strain of the A-type, the PR 8, present in the Puerto Rican epidemic of 1934. In 1940 he went on to detect a completely distinct type, B, with no immunological relationship to the A-type.

The US Army, fearful of a repeat of the 1918 flu epidemic, set up in 1941 a commission to develop a vaccine and asked Francis to be its chairman. By 1942 he was ready to vaccinate 8000 soldiers with his vaccine but, perversely, flu was scarce that year. It was not until 1943 that he was able to report that those vaccinated were 70% less likely to be hospitalized compared with the control group. This encouraged the army to vaccinate some 1,250,000 troops in 1947 but this time it disconcertingly seemed to offer no protection at all.

It soon became clear to Francis why the vaccine had failed – the arrival of a new strain of A-type virus, known as A¹. Francis was thus able to present the dilemma facing flu epidemologists, namely that while it was certainly possible to develop a vaccine against flu it was more than likely that it would end up as a vaccine against yesterday's flu.