One important factor to consider is the historical context surrounding the ring. The words "Liberte, Egalite, Fraternite" are part of the national motto of France, and they were officially adopted during the French Revolution in 1789. The presence of these words suggests that the ring may have some historical significance, which could potentially increase its value.
The year 1918, inscribed on the ring, is also significant. It marks the end of the First World War, a major conflict that had a profound impact on France. This date may add to the historical value of the ring and make it more appealing to collectors.
Lastly, the ring being a "Republique Francaise" ring suggests it may be associated with French politics or government. It's possible that the ring could have been issued as a commemorative or symbolic piece during the republic's early days, potentially enhancing its value.
Given the potentially significant historical and cultural associations, it would be advisable to have the ring professionally evaluated by a reputable appraiser or an expert in antique jewelry. They will be able to provide a more accurate estimate of the ring's value based on their expertise and the specific details of the piece.