Almost certainly better to buy ordinary tickets. You would have to pay some large supplements on that journey, some of which can approach the cost of an entire ticket.

If your family includes children under 12, that might change things. As they get a free Eurail pass with yours, and just have to pay the supplements.

That is what I am  thinking buying separately tickets.  My “kids “are 15 and 19 so no free Eurail pass for them. Thank you for your comment.

It all depends on when you will be travelling. If you book well in advance it can be cheaper with ordinary tickets. You just have to make the calculation yourself. 

If you just look at the Eurostar, an ordinary ticket can cost from about 50 EUR to more than 200 EUR in 2nd class. A seat reservation with Eurail is about 30 EUR.