I think she's making herself sound insane citing Gumtree, because IMO the truth is in it's own way worse. But I may be being unfair and she is just a fantasist.
To me the truth is more likely to be she would have either conned and endangered some poor sap by offering a 'position' that started by traveling to France with dodgy paperwork/ or hidden baby with wild story explaining it all, and then instead of 'becoming the live in nanny in a DIY Chateau program once we get there' or some other ornate lie that offered something tempting and unusual, then sacking them once there. (My first two live in plus my kids, housekeeper/nanny jobs were a steep learning curve)
Or she'd have turned to dodgy networks to find someone desperate for money who had a small baby so could raise a babies passport, and offered them serious money to go out with her child on their child's paperwork, and return without it.
But she can't say any of that because it would show up that she'd: A) endanger and entrap some poor sap trying to better themselves, or B) proposition and use someone desperate with much lower circumstances than herself, and C) have entrusted her baby to any other parent willing to do it as being 'good enough' cause they've had a kid, (or had someone close to them who had) so...
Or she lives in her own fantasy where others just do as she has planned to suit her, but also I can't help but wonder if she isn't hoping to end up in a MH setting rather than prison.