Find My Friends gets the picture from your iCloud account, if you didn't change this. If possible, sign in to iCloud using a browser - that's not possible on your iPad in Safari, you can use Puffin, if you want to use your iDevice - and take a look at your profile picture. It should be possible to change it there as well.
If your iPad is up to date, you're able to change the image in Settings - iCloud. Tap the arrow next to the email address where your (wrong) photo can be seen, enter your password, then tap Edit at the top right. Below the image, you'll find "Edit" as well afterwards. That way you're able to use a picture from your Photos app.