When Edith Piaf got hold of songs she transformed them for smoky, intimate Parisian cafes. She unwrapped tales of hookers, drunks and women scorned –pursuits always too close to her heart – and sang as if her life depended on it. Sadly, as it later transpired, it did.

French Canadian Martha Wainwright, daughter of folk singers Loudon Wainwright III and Kate McGarrigle, has taken her favourite chanteuse’s rarer songs, the ones she felt her husky, rangy voice could complement best, and is touring them around half-empty concert halls in England.

The Guardian reported on Wednesday that her show at Gateshead’s The Sage had rows of empty seats, and Brighton’s Dome Concert Hall had a similar sparseness. Upstairs was as empty as the Languedoc; the stalls were little more than half full.

Close your eyes, though, and you were almost there in post-war Parisian dancehalls, with a waif sparrow in a little black dress commanding the stage, grown men fighting back the tears, Jean Cocteau and Yves Montand sipping vermouth. But open your eyes again and the physical presence of Martha Wainwright was more Marilyn Monroe than Mademoiselle Piaf, her peroxide blonde bob and two-piece blouse suit, glamour and big-time State-side sex appeal being thrown about the stage with unreeling abandon rather than coquettish tease.

Her main qualification is the voice. Wainwright sings better in French than English. Even the one solo song she played in the encore, This Life, sounds better in our neighbours’ language, and her voice teased every last pang of pain, joy, optimism and despair from Piaf’s powerful lines.

The big numbers were absent but the show was better for it. Perhaps deep down everyone was hoping her three-piece band – guitarist and clarinettist Doug Wieselman, Wainwright’s husband and double bass player Brad Albetta, pianist Thomas Bartlett – would roll out a rousing La Vie En Rose or Non, Je Ne Regrette Rien, as they had La Foule and Marie Trottoir. But Wainwright is more than merely a tribute act. She may be a fan, but she chose songs such as Non, La Vie N’est Pas Triste and a beautiful sweeping version of Soudain Une Vallée, which filled every one of those empty concert hall spaces.

Piaf is intriguing because she found such popularity outside France. Her songs are as important for the stories as for the melody. But how many of us could say we understood the words as well as the sentiment?

Wainwright made the evening intimate by treating us to the titles and the bent. Listening to Michel Emer’s 1942 L’Accordéoniste knowing it trails a prostitute who has fallen for an accordionist entertaining in a bar, who is then dragged to war, and cannot be replaced, adds another dimension to the melody.

The only sadness, despite her playing two songs written by her late mother Kate McGarrigle, was so few people were present to see it, which begs the question: should Wainwright have done more promotion or is Brighton still a small to medium-sized non-rock concert venue short?