So far, Francis has not made any claim for an action that actually differs from current church practice and law. (He has used language that is more humanitarian than theological and there is a group of conservative bishops who are seeking to have him clarify his comments.)
I have no idea whether the church “should” convene another council. Politically, within the church, anyone who argued for such an event would probably have the action backfire on them. The Second Vatican Council was called by Pope John XXIII in 1959 and was actually conducted between 1962 and 1965. What is not understood about that council by many people, including a huge number of Catholics, is that the ideas discussed and changes made as the result of the council had been percolating under the surface of the church for at least 50, (and some would say 89) years. European culture had changed dramatically since the 16th century Counter Reformation of the Council of Trent. Secularism (that had begun in the 16th century) had become a general cultural movement. The Age of Exploration had brought large numbers of non-European people into the Church resulting in a number of ad hoc adjustments to the expression of church ideas to make the message of the church more understandable to the non-European peoples (often troubling the European-based hierarchy). The very change of European society from agrarian to industrial had challenged older expressions of church thought. And the rise of racism, the horror of (industrialized) world war, and the threat of world-ending nuclear war all became issues that the church felt a need to address.
However, every one of those issues had been addressed by numbers of theologians and pastors throughout the decades prior to 1959. No statement issued from the Council was a new invention. (This, unfortunately, was a surprise to many Catholics who had not been aware of these discussions and a number of people reacted as if the Council had simply made up new rules out of thin air.)
Issues addressed by the Council included changes to make the Liturgy more participatory by the congregations, rethinking and addressing the issues of secularism and church-state interactions, racism, (to some extent) sexism, ecumenical relations with other Christians and relations with non-Christian belief systems, issues surrounding the rise of “total warfare,” education (both of Catholics and of priests, particularly), colonialism, and several other issues regarding an old church in a changing world. Changing the position of the altar and changing the celebration of the mass from Latin to the vernacular were the things that caught the attention of most American Catholics, (since they saw those changes weekly), but a lot more went on than those changes.
Reiterating my earlier point that all the changes published from Vatican II had been in serious discussion for decades, I would guess that the sort of discussions that Pope Francis is suggesting will need to percolate for several more years–with many theologians and bishops wading in with opinions–before the church is ready to convene a new council to address them. Were such a council called today, the results would tend to simply cast current practices in absolutist terms. With the shift in active church participation moving away from Europe to South America, Africa, and to a certain extent, Asia much of the church hierarchy is actually more conservative on some of the issues mentioned in the OP than European and North American hierarchy (Lincoln, NE and St. Paul, MN, notwithstanding). The issues have not yet been discussed for a sufficiently long period to give rise to a universal consensus.