Sagna was forced off during the Gunners' 3-3 draw at home to Norwich on Saturday, with the challenge leaving manager Arsene Wenger outraged.
And with Sagna's hopes of representing Les Bleus in Ukraine and Poland next month ended, the right-back has hit out at Johnson.
"He trod on my leg," Sagna is quoted as saying. "I think he did it on purpose."
Sagna suffered a similar injury in October and he is vowing to come back stronger.
"The play carried on and I got up," he said. "When I went to control the ball, I felt a crack just like the first time against Tottenham.
"He trod on me in the same place as the previous fracture was. That's what caused the pressure. It cut in two. Now I'll start all over again. I've come back before and I'll come back even stronger a second time."
Replays appeared to suggest the collision was accidental and Norwich boss Paul Lambert has backed Johnson.
Lambert said: "There's nothing in that, it's not malicious."