By "finalism" do you mean teleology? I don't think there is an inherent flaw that problematizes all teleological narratives per say, however, teleology does present some conceptual and analytical quandaries. I mean, everything you write must start somewhere and end somewhere, that is just the nature of history. However, when your narrative is presented as events, actions, people, and trends all marching toward a definitive end point, it is quite easy to create connections that are either not really there or strenuous at best, and more problematically, ignore and under develop the contingencies within your narrative and within the historical time period you are studying. Historians like to put things in neat boxes, but the reality is historical pressures overlap, intersect, and interact. History isn't a line, it is not point A to point B. History is more like a tree, with branches, connections, dead ends, and nuances.

So to answer your question: yes, it is possible to avoid teleology. This doesn't mean you don't use periodization in your work, rather, it is say that the conceptual paradigms you use are vital in avoiding a teleological argument. I think the biggest reason you are having a hard time with teleology is that you are looking at history as a narrative of causality, rather than a narrative of exploration. If you are examining say, the causes of the French Revolution, than your project is naturally going to lend itself to a teleological framework. You are actively seeking to bridge point A to point B. However, if instead you were examining say the global ramifications of the French Revolution, you are exploring the differing impact of an event and all of the nuances and contingencies therein. So generally speaking, if someone criticizes a work as teleological, it is more of an indictment on the limited and often times simplistic conceptual framework the author decided to utilize.

In my papers I always write an "outro" on what my piece didn't touch upon (but is relevant for the whole picture) and may give a very short and general outlook on what to come, specially to avoid this finalism.

I mean, the french revolution is kind of unfair, because it very much is a final point for the long duree. It changed France big time, just like say, the creation of Germany. But there are maaaaaany things that don't lend itself to this final points, especially if your work has a more specific aim, like for example social or economic history. The economic and social make up of a given society changes much slower and way more gradual than the political make up.

A piece on french agrarian society up to the french revolution doesn't lend itself very much for a "final point".

To some extent it is inevitable as history requires that we give a narrative to a series of events and facts. For many historians this was perfectly reasonable as they saw the discipline teleologically (as the triumph of the nation, the working class or the divine will for example) but that is firmly out of fashion. Some strategies that help involve reducing ones dependence on chronology. For example thematic treatments allow the historian to deal with disconnected issues. These tend to be less popular with readers because they are harder to read.

For me this is the great challenge of History as it is where art meets science. There is an art in gathering empirical evidence to build a convincing picture of the past but it has to be done in a convincing way.

First, where did you get the term finalism? Googling "finalism history" brings up the wiki page for teleology and this thread on reddit. It hardly seems widespread.

I think you may be misunderstanding the major criticism of teleological history. The issue isn't that it follows narrative threads to conclusions. That's an unavoidable part of our field. Rather the problem is that it presents outcomes as inevitable. The French Revolution certainly happened, to take your example from elsewhere, and events from the past certainly led up to it. After the Revolution, events continued to happen, partially in reaction to the Revolution itself. There is no issue with asserting that.

The issue would arise if the historian presented the French Revolution as an unavoidable event of the historical process. This happens quite often with the American Revolution, not usually from academic historians but amongst popular commentators, especially people who see America as a nation blessed by God. America is, in their version, the inheritor of the Great Western Tradition and the Blessings of God, shining like a city on a hill, showing the world what Liberty truly is (this was the arc my high school history teachers chose!), and thus historical events were all leading up to the founding of America as the culmination of God's will. That is where finalism is problematic.

In my opinion, the best way to avoid outright teleology is to attempt to show how the themes that you are highlighting in the work continued beyond the end of the narrative. I recently finished Heather Cox Richardson's West from Appomattox. While she primarily focused on Reconstruction and definitely ended the book with a culmination of her themes, her epilogue showed how those themes continued all the way up to the 2004 Presidential election. While there is much less detail to the themes after 1901 (when she ends her main work), it still avoids any concrete sense of teleology.