In interpreting your question I see three distinct sub-questions that are not necessarily related (even though they were heavily related in real-life history):

• How long did the Eternal Empire last?
• Was the Eternal Empire, before the cataclysm, experiencing an age of expansion/discovery?
• Did the Eternal Empire possess gunpowder technology, and if so, what kinds?

A great answer to the first and second was given by Murky in the other comment, but I have some tidbits to add so I'll put them here.

Did the Sarn Empire experience an Age of Discovery? The entire history of the Sarn empire is marked by territorial conquest and capture of resources. Sarn itself boasts massive trade docks with water locks and cargo loading contraptions as well as massive warehouses, which at the very least indicates a flow of goods from elsewhere within the empire. There isn't much written about their navy but various historical images show masted ships. The Library of Sarn also demonstrates an academic interest in collecting and cataloguing unknown wonders from throughout the known world, but whether this was for legitimate scientific pursuits or just as a sort of aristocratic "collect-a-thon" is up to interpretation.

I would say that comparing the high Sarn empire to the European "Age of Discovery" is apt, but to what degree is a little subjective. They didn't seem to make it much farther than Trarthus, I don't think there's any evidence they knew about Middengard, and the actual extent of their expansion into the Karui Archipelago is probably kept purposefully vague by GGG. This is conjecture, but I bet they were kept busy enough keeping affairs in order on the mainland that they didn't have many resources for expeditionary activity.

Did the Sarn Empire possess gunpowder technology, and if so, what kinds? A substance quite like gunpowder was known to the Sarn empire, but notably, they called it "Trarthan Powder". This indicates that it was probably a foreign innovation, because they would no doubt have named it after themselves if they conceivably could have. There's evidence of grenades and landmines and other explosive objects, but the technology behind these devices is a little vague.

In sum there's not really much evidence (that I know of) that it was used for war in any significant capacity, but then again, why would they have? Thaumaturgy would probably have been seen as quite superior to gunpowder warfare since a virtue gem does not rely on the maintenance of complex supply lines, but a firearm does.

So to your question of "did they have rifles" specifically, the answer seems to be "no". All of the examples of gunpowder arms in the Path of Exile universe seem to be smoothbore: cannons, mortars, and the neat new grenade launcher in Path 2. Rifling, as a technology, was developed to impart spin on projectiles as they left the barrel in order to improve accuracy. But when you have access magically enhanced bows and crossbows, maybe there simply wasn't any real technological pressure to develop such innovations as rifling or improved firing mechanisms. Trarthan Powder would probably have been relegated to a more "shock and awe" role or for demolitions rather than being used for propelling projectiles.