I don't think anyone would doubt that it would be crazy to provide an almost open border for asylum seekers looking to come to the UK, although with the numbers crossing the channel, the border isn't far off open to those prepared to undertake the boat crossing, given the lack of willingness of the French police to pay any more attention to it than the occasional boat sabotage for media effect. However, although we might despair of lack of French support to stop the boat crossings, they do have a point when they say we ought to be looking a lot more closely to our own country, in terms of the incentives we provide for them to come here.
This said, I don't want to digress too much into boat crossings. Suppose we were to make it considerably less attractive for asylum seekers to come to the UK, and couple this with joining the EU and Schengen, then we could focus on whether or not it would make sense to provide services to more places via the Channel Tunnel as per the OP. If those ifs are too great, then sadly this thread might not be going very much further than a theoretical exercise