If it's the same as the other Peugeot keys it's a standard CR2016 battery which is used in watches, cameras, key fobs, etc.
To replace it simply unscrew the retaining screw in the keyfob and prise the two halves apart. It is sealed with a rubber seal so it can be quiet stiff. You can then get access to the battery and replace it.
This is assuming it's the same as the other key fobs I've seen.
As with most low consumption devices (such as smoke alarms, calculators, etc) the manufacturers recommend replacing the battery every year, even if the battery is still usable. The actual life of the battery will depend on many factors, such as how often you press the button and for how long you hold it down. Probably the biggest drain is accidentally pressing the button in your pocket for hours at a time.
jus thought i'd mention that i hav a '97 mondeo, and it has the same batt in the key fob, its been very heavily/frequently used over its lifetime (over
6yrs) and has only ever had one batt change and that was just over 2 yrs ago, so your batt should last some time!!
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