But they were unsuccessful in their attempts and Charlie died last July, a week before his first birthday.
He had suffered from a rare genetic condition called mitochondrial depletion syndrome, which causes progressive muscle weakness and brain damage.
Mr Gard said that before his son's death he had promised the child he would "care for and look after" the youngster's mother.
He wrote on Facebook: "Just a couple of hours before Charlie passed away, I laid on his bed, held his hand and had a little father/son chat with him.
"I told him many things. I told him how much he was loved, how much he would be missed and how proud we all were of him, amongst lots of other things.
"I also made a number of promises to him. Ones that I will never break. And one of those promises I made was that no matter what happens, I would always care for and look after his gorgeous mummy for him..
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The researchers said associations between late-life participation in intellectual activities and decreased odds of developing dementia have been reported in other studies.
Their study was conducted through Elderly Health Centres in Hong Kong, where 15,582 Chinese individuals, 63.9% of whom were women, were first evaluated in 2005. Follow-up assessments were performed from 2006 to 2012..