According to Air Transat
According to Air Transat:
"Travelling from Canada
For domestic flights, all passengers must be in possession of government-issued photo identification. Children under 16 should carry proof of identity, if no photo ID is available. For international flights, depending on the requirements of the destination country, each passenger must be in possession of proof of citizenship with photo ID in the form of passport, birth certificate and driver's license, or citizenship card. Please consult your travel agent for specific country requirements. Here's a helpful checklist of passport and visa information you may want to check out before you leave."
If you are travelling with a birth certificate only, they will ask for another id that has a photo on it.
If everyone in your party has a official birth certificate and a valid driver's license, then there should be no problem.
However, on their website, Air Transat recommend that all passengers travel with a valid passport, regardless of their destination.
I also checked Signature Vacations. They too are recommending a passport. "We strongly recommend that you travel with a valid passport. Where a country allows Canadians entry with a birth certificate, you will also be required to provide photo ID (such as a driver's licence). "
Maryanne