Did Professor Snape jinx Harry's broom during his first quidditch match?

No. Professor Quirrell, the Defense Against the Dark Arts teacher secretly in league with Lord Voldemort, jinxed Harry's broom in an attempt to hurt him since Harry was responsible for Lord Voldemort's downfall a decade earlier. Hermione mistakenly believed Snape was jinxing Harry's Broom when she saw his mouth moving when in fact Snape was trying to save Harry by issuing a counter-jinx.