Lydia Drake and her husband Roy started the business more than 40 years ago, and the pair are looking to pass on the business to new owners.
An advert for the business posted on Facebook attracted more than 200 comments from customers worried their local bakery would close.
Lydia said the pair had been looking to sell the business for more than a year, but 'if the new owners won't keep it open as a going concern' they would not sell.
The 67-year-old said: 'We are thinking of maybe retiring.
'But we've had no real interest in it as a going concern.
'If we cannot get someone willing to take it on as a bakery, we're not interested.'
Lydia said she was 'not sure' why the advert for the business had been shared - or why it had been removed.
She added: 'There are lots of nice comments though.'
The Drakes are looking for a 'traditional' baker to take on La Boulangerie for £95,000, with the pair to remain as lease holders.
The price includes the whole business and stock, including a a four-deck oven and two proofers.
The advert, hosted by Hilton Smythe, describes 'demand in the area for deliveries, off van sales and celebration cake order', adding there is 'a full handover' for any buyer.