He was the son of Captain Godschall Johnson (1780–1859), formerly of the 10th Royal Hussars, and his wife Lucy (died 1823), daughter of Sir Cecil Bishopp (1753–1828) 8th Bt., of Parham Park, West Sussex; 12th Baron Zouche.

He was elected a vice-president of the British American League in 1849, and opposed the Rebellion Losses Bill later in the same year.

In 1854, Johnson was commissioned by the Hudson's Bay Company to work as a legal administrator in Assiniboia.

On October 21, 1870, Lieutenant Governor Adams George Archibald appointed Francis as a legislative councillor in the North-West Territories.

The appointment to the Temporary North-West Council was quickly revoked by the federal government, however, which ruled that Archibald had overstepped his authority in granting it.

This appointment was also revoked, following opposition in the House of Commons of Canada to a government appointee holding two paid positions.