How to Tell Whether the Alagard Font Is Actually Applied
Because the pack only swaps a font, it is easy to enable it and see no obvious difference if something is overriding it or if you are looking at the wrong text.
Look at the Right Places
Check the chat window, a sign, an item tooltip, and the title screen. All of these use the game font, so if the font changed, all of them should look different. If only some changed, something else is overriding part of the font set.
Compare Against Default
Temporarily disable the pack and look at the same screen, then re-enable it. Side-by-side comparison is the fastest way to confirm the change, especially if you are unsure whether the ornate letterforms you are seeing are Alagard or another pack.
Common Reasons It Looks Unchanged
First, another resource pack is loaded above Alagard and winning the conflict. Second, the pack failed to load, which you can check in the resource pack list for an error indicator. Third, you are looking at text rendered by a mod that supplies its own font rather than the vanilla font. Reorder packs first, then test again.