There are different ways to go to Wrexham from Paris:
It is possible to arrive by car in 8 hours. In this case, take the A16 then the Channel Tunnel (30euros), the M20 until Ashford, then the M40, M51 and A41 and to finish M525 until Wrexham.
Google map
From Paris, you can take the Eurostar (50€) to London and after a local train from London to wrexham (£13 or 20€). The trip takes about 6 hours.
It is also possible to go by plane to Liverpool (50 €) and by train to Wrexham (£8 or 10€). The trip is composed of an hour and half of flight and an hour of train.
Sources: https://www.eurotunnel.com/, https://www.easyjet.com/fr, https://www.eurostar.com/