Unfortunately Eurostar runs airline-style pricing so the cheaper tickets generally sell out well in advance of travel. At just five weeks out from travel sometimes the very early morning trains (5am) are still cheap, but not on summer weekends.

Flights for your date are priced around half of the cost of the train at present - something like €130.

Another option: you could try one of the long-distance bus companies (eurolines, megabus, iDbus) who will charge something like €50 or €60 per person. Beware that the journey time is very long and can be cramped.