“Vive la France!” says Bernard Sumner as New Order take to the stage with a large tricolore illuminated brightly behind them. The fervent applause goes on and on. It’s the fact that Sumner is such an everyman figure, and New Order the most human and empathic of bands, that makes his gentle words so moving.

The veteran Manchester group recently enjoyed their highest charting album in more than 20 years with Music Complete, a record that moves them firmly back towards the wistfully charged rave-pop of their 80s and 90s peak. The galloping synths and existential ache of tonight’s set opener, Singularity, evokes career high-water marks such as their 1989 Technique album.

The ingenuous Sumner is a perennially boyish figure even as he stands on the brink of turning 60. Shuffling from foot to foot, he looks endearingly ill at ease as La Roux singer Elly Jackson joins him to duet on the exuberant Italo house of new tracks Tutti Frutti and People on the High Line.

Plastic is all motorik pulse and Moroder bleeps and gurgles, but it is when New Order delve into the electro alchemy of their peerless back catalogue that they are nigh on untouchable. True Faith still appears to be mainlining pure serotonin, while the set-closing Temptation celebrates love’s exquisite infatuation that always lies a hair’s breadth from despair.

Returning for the encore, Sumner dedicates the sepulchral shimmer of Joy Division’s Atmosphere and the desolation of their sacred-text angst anthem Love Will Tear Us Apart to the Paris victims, before New Order close with their defining dancefloor monster from their younger, innocent days, Blue Monday. Just when it was needed, they have delivered us a profoundly life-affirming evening. The show will go on.

• At O2 Academy, Glasgow, 19 November. Box office: 0844 477 2000. Then touring.