Brachet was educated at the Free University in his native city of Brussels where his father, an embryologist, was rector. After gaining his MD in 1934 he joined the faculty as an anatomy instructor and in 1943 was appointed professor of general biology.

Brachet began his career by studying the then poorly understood nucleic acids. It had been thought that plant cells contain RNA and animal cells DNA but, in 1933, Brachet demonstrated that both types of nucleic acid occur in both plant and animal cells. He proved this by developing a cytochemical technique that made it possible to localize the RNA-containing structures in the cell. Brachet also noted that cells rich in RNA tend to be those actively engaged in protein synthesis. On this basis Brachet was led in 1942 to propose the important hypothesis that ribonucleoprotein granules could be the agents of protein synthesis. Such granules, later termed ribosomes, were indeed shown to function in this way by George Palade in 1956.

Later experiments, in which Brachet removed the nucleus from the cell, showed that although protein synthesis continued for a while the amount of RNA in the cytoplasm decreased until there was none left. This indicated that the production of RNA occurs in the nucleus and that it is then transported from the nucleus to the cytoplasm.