A video will help you figure out what gait she's doing at that particular time, but it's better to learn how to feel the gait. A lot of horses will switch gaits based on tack, rider, footing, mood, etc.
Here's a video of my mare foxtrotting, so you can compare:
It is possible to feel what she's doing. In a foxtrot, you should feel a slight front-to-back motion. With square gaits (rack, running walk, etc) you'll feel a slight up-and-down motion. With lateral gaits (pace, stepping pace), you'll feel a side-to-side motion. The foxtrot will feel very smooth, but you'll be able to feel a slight bump in the back of the saddle when she lifts her hind legs. Her head should bob (which helps you to differentiate between the foxtrot and the stepping pace - where the head is held still). If you turn around, her butt and tail should also be moving up and down - something that is absent in ALL other smooth gaits.