The Payconiq by Bancontact app works entirely independently from the SIM card in the device. This means that provided your mobile phone number has not changed, replacing your SIM card will have no effect on use of the app.
You can change the telephone number yourself in your app's settings. Go to Menu, Settings and under Profile, tap on your current telephone number, where you can change your telephone number. If that doesn't work, send an e-mail to firstname.lastname@example.org