First point: I really haven't enough information on the liturgical thought and practice of the new pope to possibly offer any informed thoughts -- so I won't comment upon that.
There are some things that I can comment upon though.
Regarding some of the vestural choices we've seen so far that people are asking about, I wouldn't care to deny that these may well send some signals about a possible direction. (The fact that such things can and often do carry 'messages' also is demonstrative of why externals certainly shouldn't be considered unimportant or inconsequential incidentally, but I digress.) Certainly we know Pope Benedict's choices did; that was made abundantly clear by Msgr. Guido Marini. At the same time, as regards Pope Francis I wouldn't care to jump to any conclusion at this point. All one can do is wait and watch and keep things in their proper perspective. At the end of the day, while I quite like some of the extra-liturgical trappings of the papal office that Benedict restored, and certainly would be glad if this were to continue, my own primary concern is with regard to the sacred liturgy proper. Of higher priority to me is that we would continue to hear the liturgical propers chanted and restored to their proper place within the liturgy; that we would see noble vestments employed (which can have various manifestations let's remember), pontificals used, proper liturgical orientation fostered, etc. I would hope that we would continue to receive good liturgical catechesis and so on. (I've already gone through my "wish list" in another post.)
However, let's hit the point that many are no doubt thinking: what if the new pope doesn't do these things? What if his "personal liturgical style" is such that the propers are not chanted, the vestments simple but not noble, pontificals are abandoned and the approach to the liturgy is overall quite "loose" by comparison? (Let me just say for the record that the idea of a "personal liturgical style" is inherently problematic since the liturgy is no one's personal possession to alter and shape at whim or will -- not even a pope's. One cannot imagine such a thing occurring within an Eastern liturgical context for example. The divine liturgy is simply the divine liturgy and they are formed to it and by it, not the other way around. This is true from a patriarch on down. This is appropriate and is the model to follow.)
Back to the question many are no doubt asking, I want to be honest that the reality is that this could indeed happen. Some or even all of these things might be dropped. The "Benedictine arrangement" might disappear from the papal liturgies. The vestments used in the papal liturgies might become simple (not an issue in its own right I'd note) but also arguably less noble. The propers could be replaced by hymns and so on. This could happen and I think anyone who is rational has always known that this could happen -- and in fact, I would say if we were really honest with ourselves, you'd actually have to say it was fairly likely. I've said it before and I'll say it again: cultures, including liturgical cultures, simply do not change overnight -- and we are by no means out of that post-conciliar liturgical culture. So why be shocked by such a potentiality? Is it happening now? It's simply too early to tell. Wait and watch as I say.
Someone might say, "but if that happens, aren't we supposed to look to the papal liturgies as models to follow?" I'd point out here an important distinction. We aren't liturgical positivists whereby whatever a pope, any pope, does liturgically must be followed or seen as the exemplar. Pope Benedict's liturgies were indeed identified as exemplars in the recent past but that was not because it was the pope's liturgy that it was an exemplar; rather it was an exemplar because they were liturgies celebrated according to sound liturgical principles. It is the principles that matter and we should keep that always closely in mind.
But back to our scenario, even if that is what is happening (which we don't yet know I'd continue to stress), what would that mean? This brings me to the crux of what I really want to say, which is in reality entirely separate from the questions people are asking me, having nothing whatever to do with this pope or any other.
I have said over the years that I believe Benedict XVI understood this point about the need not simply for legislation, but rather for a renewed liturgical formation and a change in liturgical culture; for there to be lasting effects you first need to change hearts and minds. Benedict knew of this cultural issue only too well (and no doubt perceived the very potentiality which we are discussing here now) and that is precisely why he sowed the particular seeds that he did I think; seeds which were planted by his liturgical teaching, his liturgical example, and by the liturgical doors he opened (such as with the Ordinariate and Summorum Pontificum for example). Doors which remain open I'd remind people -- and which really aren't that easy to close pastorally speaking.
Benedict, while the "father of the new liturgical movement" (in my estimation at any rate), is not the new liturgical movement; as such the new liturgical movement does not die with the end of his papacy. No, the new liturgical movement is not based on a person or personality; the new liturgical movement set in motion by him is just that: it is a movement and one based on liturgical first principles. That movement continues to exist now and, as it always has been, is mainly operative at the grassroots level amongst laymen and women, amongst seminarians and amongst the clergy -- especially the younger clergy. While I wouldn't care to deny that it is certainly helpful when the pope is himself bearing the standard of this new liturgical movement, it is not a make or break point at the end of the day -- and for that reason, as interesting as it will be to see how the papal liturgies unfold over the next years, more crucial will be what is happening on the ground at the parish level for it is ultimately there where the new liturgical movement is based at this stage of its life; there and in the writings and researches put forward by the liturgical conferences we have spoken about, the books and periodicals that are put out, etc. As it was in the 20th century Liturgical Movement, so too again now.
In this regard I can only offer my encouragement that you forge on with the movement that was seeded and fathered by Pope Benedict XVI but which was always destined to have to outlive his own particular papacy, not to mention many others. Take courage in that reality and realize that we could never expect this to be simply handed to us from on high (a source of frustration for some even under the last pontificate). Tools were given as we still have those tools; now we need to utilize them and from them draw out further gains and progress. All of the tools and gains we have seen, from the new English translation of the modern Roman missal, to Summorum Pontificum and the Ordinariate, to all of the grassroots resources that have sprung up to help people learn to sing the propers again and so on, none of these things have ceased to exist; nor have they become redundant. Far from it. Our task is clear: like a gardener we must now tend to the garden, watering and fertilizing those those seeds and tending to the green shoots. Let's focus on the tasks at hand, for the success and future of the new liturgical movement is not opened for us solely by the keys of Peter (which have already opened much for us as I have already said), but also by the keys of every parish priest within his parish, every religious within their monastery or religious house, and every layman within their own domestic church.
To end on a lighter note, I've noticed this internet meme for some while on the internet and perhaps a picture really is worth a thousand words and this get across what I am basically trying to say here: