The journey time would be 3 and a half hours each way if there was passport control at Manchester, closer to 5 hours if people need to get off the train to go through passport control in London or Lille. Its too long by at least half an hour if not 45 minutes to an hour. I come back to my main point that the service could probably attract enough passengers to fill a service or two a day but not enough to be commercially viable or be worth losing paths for domestic services on HS2.
Taking into account that a Manchester / Leeds - Paris service would be city centre to city centre, 3.5, even 4 hours really isn't that bad. Considering that flying you would have to take into account the 2 hours you would have to give for checking in & security, a 1 hour or more flight, then probably another 30 minutes on the other side just to reach your transit, and then transit time you could probably set off from home from many places in the North and still arrive at your hotel in Paris at around the same time, be it by plane or train.
Security and passport control is obviously an issue, but given that all HS2 stations save Euston & OCC are brand new builds, if a link were to be offered would it really be that difficult to incorporate a scanning & security system, and some system of isolating platforms due to be served by international offerings? Given the overall cost of the build, it really wouldn't add that much at all.
As for demand, the biggest mistake often made by people is that they look at current demand & assume that it will by in large stay the same. But people's habits are changing, city breaks are getting ever more popular and though there are lots of low-fare seats out there the reality is that many people booking don't get the cheapest ones. And once you start to throw in things like extras for baggage, airport taxes, even car parking or the cost of getting a taxi to the airport, the price can soon rack up. If a future HS2/HS1 operator could find use of some off-peak capacity to extend services to places like Paris from the Midlands and the North, I'm pretty sure a new market would emerge. After all open access operators like CG can offer much longer transit times than VTEC to the capital from some locations, yet people do still use them.
Its probably not what people want to hear, but one of the risks of HS2 is that it's prime purpose simply becomes a new commuter line from London, with its peak flows being to the capital in the morning, and in the opposite direction in the evening peak. This could lead to a lot of "fresh air" being carried up and down the lines given that HS2 offers far more London-bound capacity that the mains it is to replace. So why not keep an open mind to the possibility of using at least some of that capacity for Euro destinations and plan accordingly? The skies around the UK are becoming increasingly congested, and in 15 years or so we might be glad of the opportunity to take some of the pressure off it.