The stunt was the latest in a series of separated parents scaling cranes across France to complain about lack of access to their children.
April Reiss, 70, said a French court had ordered the girl's Belgian mother to let her see her during a two-week period but that she was refusing to comply.
"My daughter-in-law is taking Rose away from me and the court isn't listening to me, so now I hope they will listen," she told AFP by phone, adding that her husband was very sick and wanted to see the girl before he died.
She said she had travelled from Connecticut to Privas in the south of France to see her six-year-old granddaughter.
The girl's father, Scott Alexander Reiss, was on Saturday at the foot of the 30-metre crane and said he had not seen his daughter in more than two years.
Privas prosecutor Dominique Senechal said the father had been charged with sexually assaulting the girl and that the two-week visiting rights were granted only to the grandmother, as the father was banned from having any contact.
April Reiss said she was accompanied at the top of the crane by a professional mountaineer.
Last month a French father denied access to his son held a four-day protest perched on a giant crane.
That stunt sparked reactions from the prime minister and the justice minister, who subsequently met with representatives of groups defending fathers' rights.