Short answer. No, not automatically. Article 626 limits the dominant estate's owner to using the easement only for the benefit of the immovable originally contemplated, and only in the manner previously established. Extending it to serve newly added farmland goes beyond what your existing easement covers.
What the law says
The owner of the dominant estate cannot use the easement except for the benefit of the immovable originally contemplated. Neither can he exercise the easement in any other manner than that previously established.
Civil Code, Article 626 — Use Limited to the Original Purpose. Read the full provision →
The easement is tied to a specific property, not to you
Article 626 anchors an easement to the property it was created for, not to whoever happens to own that property at a given time. It states: the owner of the dominant estate cannot use the easement except for the benefit of the immovable originally contemplated. Your right of way exists to serve your original farm, the specific immovable the easement was set up for. It is not a general benefit that automatically follows you into whatever additional land you later come to own or use.
Expanding the farm does not expand the easement
Because the easement benefits the immovable originally contemplated, adding new land to your farm does not, by itself, extend the easement's coverage to that new portion. The right of way remains scoped to the property it was created to serve. If you now want to route traffic through your neighbor's land specifically to reach the newly added land, you are asking the easement to do something beyond what Article 626 allows it to cover on its own terms.
The manner of use is also fixed, not just the property
Article 626 adds a second restriction that matters here too: "neither can he exercise the easement in any other manner than that previously established." So even setting aside the question of which land benefits, how the easement is used, such as its route, width, or purpose, is likewise fixed by what was originally established. Using the existing right of way more intensively, or in a different way, to accommodate the expanded farm operation can itself run into this same limitation, independent of the question of new land.
What this means for your expanded farm
If you want the right of way to also serve the newly added portion of your farm, Article 626 does not get you there automatically. Extending the benefit of an existing easement to additional property, or changing how it is used, is a change to the easement itself, not something that happens simply because your farm grew. Serving the new portion would require a separate arrangement with your neighbor addressing that specific need, rather than treating the existing easement as if it already covers it.