No, the Church is not infallible because the Pope is infallible. It’s the other way around.
There appears to be a lot of confusion about the origin of the Pope's infallibility - let alone when it is in force.
Here's a quick summary in this time of darkness!
Source:What's Up With The Synod?
The Pope has the keys. He can even command us what to think. Or rather, he can bindingly declare what Christ has taught, and therefore what God has said, and requires that we believe. But Christ will NOT let His Church be bound into error. So…
When the Successor of Peter, teaching on a matter of Faith and Morals, AS Successor of Peter , binds the universal Church to believe or to absolutely and “definitively ” hold a particular truth, he shares in the infallibility of the Church.
We are only required to believe that the Pope is infallible when all the above conditions are fulfilled. We are very safe in following the teaching of Pope Saint Pius X, in his Catechismo maggiore, that the pope is infallible “only” (soltanto) under those conditions.
From the “Catechismo magiore” of Pope Saint Pius X:
199. Quando è il Papa infallibile?Il Papa è infallibile allora soltanto che nella sua qualità di Pastore e Maestro du tutti i cristiani, in virtù della suprema sua apostolica autorità, definisce una dottrina intorno alla fede o ai custumi da ternersi da tutta la Chiesa.
“soltanto” = “only,” as in, “at no other time or in no other way”.
This means it is impossible for the pope to *bindingly* contradict the constant and very firm teaching of the Church.
But by ambiguity, implication, association, action, or in other ways, the pope can sow doubt. As unfortunately we have been seeing these days.