Born in London, Barry was educated at Harrow School after his mother's death at the age of two. His father, Sir Edward Barry (2nd Bt) remarried soon after, leaving the young Barry to a series of relatives, tutors and doctors who left him in something of a muddle as to his health and relevance (though ultimately he would inherit the baronetcy). After two years at Harrow he had a nervous breakdown, but was not allowed to lodge at home where there was a new family.  Art seemed to offer him the growth and direction he needed, and in 1900 he enrolled in classes at  Bournemouth School of Art where he met the first of his two future wives, Doris HUME-SPRY. 

Privately he studied with Sir Alfred EAST, whom he was to regard throughout his life as mentor and friend.  East had previously studied and worked alongside Stanhope FORBES at Newlyn, and encouraged the young Francis to head to the area to gain inspiration and confidence. This met with parental approval, as the Newlyn reputation flourished. In 1906 his first paintings were accepted at the RA, and he joined the RBA. He also sent to the Royal Society of Scottish Artists and the Paris Salon in Paris, where his work was well received.

The following year (1908) at the age of 25 he married Doris, and the couple moved from Newlyn to St Ives. Three children, Kathleen (1909), Rupert (1910) and Sheila (1915) were born there. From 1910 he exhibited irregularly at the Paris Salon, showing 9 paintings in all, until 1939. In 1911 he exhibited at the NAG Winter show.  In 1912 in St Ives he showed The Sunlit Harbour (St Ives) before sending it to the RA, and in 1913 he exhibited Windsor Castleand St Ives, the new town. From this time his style began to move from the narrative (Newlyn) style to landscape, and his interest in etching developed. Frank BRANGWYN was one of his tutors in 1916. On Show Days in St Ives he shared exhibiting studios with his wife who created highly-regarded needlework and textile art.

In 1922 Barry left his wife and family and travelled to France and Italy, concentrating on etching. His first marriage was dissolved in 1927, and he remarried, his second wife being Violet Gwendolyn Pretyman. He continued to exhibit at the Paris Salons, and merited Gold, Silver and Bronze Medals for etchings shown both in Italy and France. By 1939 he had returned to St Ives where he joined the St Ives Arts Club and took over Fred MILNER's studio at 2 Piazza (See Tovey 2009 p163, Fig.2.152 for a photo of FB in his Studio in 1945, with paintings). After the war (in which his etching plates left in Italy were destroyed in a bombing raid) and after holding his final exhibition in St Ives, he and his wife moved to Jersey. In 1946 he inherited the title of Third baronet.