With the hosts 14-9 ahead at the break, France wing Yoann Huget picked off Weir's attempted pass to Alex Dunbar, racing 80 metres to score and overturn the lead.
Weir hit back from the tee a quarter of an hour later but a last-gasp Jean-Marc Doussain penalty secured a third French win of the 2014 RBS 6 Nations.
The incident came in contrast to a fortnight before when Weir was Scotland's hero, kicking a last-minute drop goal to beat Italy in Rome.
However, Johnson believes the 22-year-old has the character to bounce back from this disappointment and produce more match-winning moments for his country in the future.
"It goes two ways with Duncy," said Johnson. "With the intercept, sure, he fell down - but the look at the guy's character. He stood up for the kick that put his side back in front.
"I like character. Sometimes it's not about execution. I can work with character. We can develop skill.
"We have backed Duncy. We haven't put another ten on the bench. We're trying to get a bit of growth out of him. He has got a basic skill set that we like.
"Yeah okay, he was unfortunate. He chose the wrong option, the wrong execution. But he showed good resolve at the end. I'll take that every day."