Emily Watts' parents, Nicky and Dominic, along with her 27-year-old brother Rory, have all travelled to the hospital in Annecy where she is being treated.
It took several days for French authorities to notify her parents because she was not wearing any form of identification.
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The controversial procedure involved nuclear DNA from the mother, mitochondrial DNA from a donor, and the father's sperm.
The move comes amid a boycott of the paper in Liverpool due to its controversial coverage of the 1989 Hillsborough disaster.
Glasgow East MP Natalie McGarry has been charged in connection with alleged fraud offences.