You're right that far breton isn't a cake that puffs up a lot, but if it's really flat and dense, something went wrong. Your grandmother's recipe definitely has baking powder or well-beaten eggs to create some volume. If you forgot the baking powder or didn't mix it in properly, that could explain why it didn't rise at all.
One thing people don't always think about: the oven. If your oven isn't heating enough or isn't heating evenly, the batter will bake without rising. It's silly but it happens. I had that happen once, and after I put a thermometer in the oven to check and sure enough it wasn't at the right temperature. Also, if you were pouring in cold ingredients or didn't let the batter rest a bit before putting it in the oven, that can affect the result.
Try again next time and be really careful with the proportions, make sure the oven is properly preheated, and if the recipe calls for it, beat your eggs well. The far should be soft and light even if it doesn't puff up as much as a regular cake.