Firefox is a fast and wonderful browser but when it comes to fillable PDFs, it does not let you fill-in the fillable form by default.
This can be more user friendly for sure and here are some options:

Option 1: Download the PDF or Open the PDF in Acrobat

After clicking on the link to a pdf file, there are 2 places you can click to download. It will be the red or yellow arrow as shown below. After clicking, select to 'Save file' (ie download) or 'Open with Acrobat'

 

Option 2: Set Firefox to always use Acrobat to open PDFs

STEP 1: In Firefox, click on the “Firefox” menu in the upper right‐hand corner of the window, then click "Options"

 

STEP 2: In the “Options” menu, click on the “Applications” tab. Then, scroll down to “Portable Document Format (PDF).” If it reads, “Preview in Firefox,” that means that you will need to change the setting in order to complete fillable PDFs.

 

STEP 3: In the drop down menu, select “Use Adobe Acrobat (in Firefox).” Then, select OK to close the Options box. Close out of your browser window and reopen Firefox to implement the change.

Now, you can fill fillable PDFs happily ever after.