Les Bleus fought back to level at half-time through a Wesley Fofana try and secured the win in the second-half as Maxime Medard went over.
Despite full-back Stuart Hogg and wing Lee Jones trebling Scotland's Championship try tally, the hosts lost their third successive Six Nations game, and a fifth straight in all competitions.
But Saint Saint-André believes Andy Robinson's men will turn their fortunes around sooner rather than later once Lady Luck decides to smile on them rather than against them.
"The difference between winning and losing is in small details," said Saint-André.
"When you look at Scotland's last four games, in the World Cup they lost in the last minute to Argentina and the try by England (in New Zealand) was in the 77th minute.
"Against England again in the Six Nations, Scotland created four or five opportunities but one turnover and England won the game.
"And against Wales they had control of the first half and then they had a yellow card and Wales scored two tries.
"We just said 'we're worried, we hope it wouldn't be us'. I'm sure Scotland will very soon beat a fantastic team because they have some fantastic players."