The brakes are feeling kinda spongy, with less bite - is that a sign the pads need replacing?

The front pads are from the previous owner (6-years ago), so no idea how long they've been on the car.

The rear pads are 2-years-new (and ceramic) and the pads they replaced had Jaguar logos on them, so could very well have been the original set since you'd be crazy (or crazy-wealthy) to buy OEM pads for an x308. If indeed they were originals, they lasted a record-breaking 125k miles!

 

You need to pull the wheels and check: minimally, a brake bleed to replace the old fluid and to check the hoses. Water in old fluid, along with air in the lines will give you a spongy brake. So will a hose that expands (paid, once, for a new caliper and busted knuckles on my wife's POS Maxima, only to find it wasn't a bad caliper, but a soft hose).

 

Wow, fascinating, but how can you tell if the hose is expanding? Is it visible when you pump the brakes?

Is there any service-recommendation to change brake fluid? It is likely the original fluid from 2002

 

Refer to the vehicle Owner's Manual for recommended service intervals. Brake fluid generally should be replaced every two years, or if it becomes very dark from absorbing moisture.

Check to make sure the calipers are sliding properly as a sticking caliper can also create a 'spongy' pedal feel.

 

Have an assistant press brake pedal and look at the movement of the caliper and hose, wheel by wheel.

But not meaning to offend: when I see questions like yours, suggests you need to take it to a shop.

 

Another thing to check for on the brake hoses is cracking. When doing my front ball joints, I found cracks in both brake hoses, next to the calipers, where the bend radius is sharpest.

I don't think cracking would cause your spongey pedal, but it is a potential safety issue.