Dan Evans’ swift 6-2 6-3 6-3 reversal to Jeremy Chardy followed Kyle Edmund’s 7-5 7-6(6) 6-3 defeat to Lucas Pouille in Rouen.
GB must win Saturday’s doubles and both Sunday’s singles matches to reach the last four – a task that looks far beyond them on Friday’s evidence.
Visiting captain Leon Smith’s task was always going to be tricky without world number Andy Murray, recuperating from an elbow injury, and the French clay – with Evans’ last victory on the red dust dating back to 2013.
And though he tried to mix up his game against Chardy – an opponent 24 places below him in the ATP rankings – the 26-year-old was powerless to prevent defeat.
Earlier, Edmund found himself on the wrong side of small margins against Pouille.
He should have levelled the opening rubber in a second set tie-break but, from 5-2 ahead and serving, Edmund lost four points in a row and then missed a backhand return on the Frenchman's second set point.
And when Edmund double-faulted twice and dropped serve again in the sixth game of the third set, faint hopes of a comeback were extinguished.
"We probably needed the win from Kyle to get us started this weekend - and we will now have to do it the extremely difficult way," Smith told BBC Sport.
Jamie Murray and Dom Inglot will face Nicolas Mahut and Julien Benneteau in Saturday's doubles.
With additional reporting from PA Sport
Read the original article on Eurosport: Great Britain’s hopes in tatters after two defeats