The company said over the weekend that it is reviewing “all strategic options in order to deliver maximum value for its shareholders”, including a potential sale.
Any deal would see founder and chief executive Stephen Marks offload his 42% stake in the chain.
Shares were up more than 30% at the market open at 56p.
Like much of the high street, French Connection has had a difficult time of late and recently posted widening half-year losses following an £800,000 hit from the House of Fraser collapse.
The group reported pre-tax losses of £15.1 million for the six months to July 31 against losses of £5.9 million a year earlier, following writedowns including the House of Fraser impact and store leases.
Complicating any sale is the spectre of Sports Direct boss Mike Ashley, who holds a 27% stake in the firm.
Mr Marks founded French Connection in 1972 and it later gained notoriety for its “Fcuk” branding.
At its half-year results last month, the group outlined proposals for a further retrenchment from a difficult high street, with plans to close eight retail stores over the full financial year, having already shut two in the first half.
It said at the time that the “continued deterioration of trading conditions on the UK high street” meant it was reviewing leases on a number of other loss-making stores.
French Connection now has around 100 own-managed stores and some 200 operated under franchise or licence.