She claims the manager failed to apologise and told her that she "should have known it was chicken" as she had taken a few bites.
But Franco said she didn't realise as she had been a vegan all her life.
"All of the staff stood there staring at me. I felt humiliated and have been left traumatised due to not only a lifestyle choice but also religion being broken and made fun of," Franco said.
"I was speechless and can't express how disgusting their customer service was."
KFC later apologised for her ordeal at its branch in Colliers Wood.
"This isn't great and we're really sorry for what happened here," a KFC spokesperson said.
"Our vegan burger launched last month and we took its arrival seriously - putting strict new processes in place to make sure it's served properly, including the use of separate coloured tongs and storage units.
"We're following up with the team to remind them of the importance of getting this right and will be offering the guest a free meal on us to put things right."