The German Railways website combines all European railway timetables and it's available in English:
https://www.bahn.com/i/view/GBR/en/index.shtml
A typical journey, based upon travel next Monday, is this:
Depart Brighton 0732
Arrive Ashford 0918
Depart Ashford 0955
Arrive Paris Gare du Nord 1247
Take Metro Line 4 to Paris Montparnasse
Depart Paris Montparnasse 1425
Arrive Biarritz 1945
[Total journey time: 11h 13m]
HOWEVER . . .
By default, that website only allows 30 minutes transfer time at Ashford and 65 minutes to get across Paris. Given that the (theoretical) minimum check-in time for Standard class travel at Ashford is 30 minutes, you might want to use the 'Adjust the transfer time' option to allow longer between trains there. meaning that you'd need to leave Brighton a bit earlier. (65 minutes to get across Paris should be OK though).
ALTERNATIVELY . . .
The Eurostar website allows you to book through travel (which can work out cheaper than booking separate trains).
http://www.eurostar.com/uk-en
Click in the 'From' field, then on 'United Kingdom', 'B' and 'Brighton'. Click 'X' to close the box. Click in the 'To' field and then on 'France', 'B' and 'Biarritz'. Click 'X' to close the box.
Doing it that way (and using a sample date in September), offers the following route:
Depart Brighton 0530
Arrive London Victoria 0702
Victoria Line to St Pancras International
Depart St Pancras International 0755. (That's a fairly tight connection but shouldn't be a problem as it's only a 10 minute Tube journey and the 30-minute check-in time is actually a bit flexible, especially if you're travelling on trains booked directly through Eurostar)
Arrive ParisGare du Nord 1117
Metro Line 4 to Paris Montparnasse
Depart Paris Montparnasse 1225
Arrive Biarritz 1746
[Journey time = 11h 16m. If you don't fancy getting up that early, you can leave Brighton, with similar connections, at 1028, getting into Biarritz at 2245]