The gathering, attended by some 300 bishops and delegates, has been preceded by intense jockeying between conservatives and liberals on a number of sensitive issues.
In his address to open the first working session, Francis said the bishops should not just talk but try to listen to what God wanted for the Church of 1.2 billion members.
In a nod to conservatives, he called for courage that "does not let itself be intimidated by the seductions of the world" and passing fads.
But, in what appeared to be a reference to unbending traditionalists, he said the bishops should also beware of the "hardening of some hearts, which despite good intentions, keep people away from God".
He said Christian faith was "not a museum to look at and save" but should be a source of inspiration. Francis called on the bishops to have "courage to bring life and not make our Christian life a museum of memories".
The bishops, who are meeting behind closed doors, will submit reports to the pope. He may use these to write his own document, known an Apostolic Exhortation, on family issues.
One key topic at the synod will be how to involve Catholics who have divorced and remarried in civil ceremonies.
They are considered by the Church to be still married to their first spouse and living in a state of sin. Some bishops want a change to the rules that bar them from receiving sacraments such as communion.
Last month, Francis made it simpler and swifter for Catholics to secure a marriage annulment, the most radical such reform for 250 years. He told bishops to be more welcoming to divorced couples.
Another topic will be the place of homosexual Catholics.
The immediate run-up to the synod has been dominated by gay issues.
On the eve of the gathering, the Vatican dismissed a Polish priest from his Holy See job after he came out as gay and called for changes in Catholic teachings against homosexual activity.
Conservative Catholics held a conference in Rome just before the synod started on how homosexuals can live by Church rules that they should be chaste, while Catholic gay activists held another demanding full acceptance of active gays in the Church.
In its explanation of the firing of the Polish monsignor on Saturday, the Vatican said his very public coming out was intended to put undue media pressure on the synod.
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