The changes to eurostar's bike policy only really affect people wanting to carry undismantled bikes. If you're planning on carrying your bike in a box or bag then it makes no difference (if you're wanting to travel with an undismantled bike then you may need to put your bike in a box provided by eurostar - not exactly a big deal).
The eurostar bike service does operate to Lille.
All non-folding bikes or those over 85cm long will need to travel with our registered luggage service, Eurodespatch. This is available from London, Paris, Lille and Brussels, and we have a couple of options for you to choose from.
http://www.eurostar.com/uk-en/travel-info/travel-planning/luggage/bikes
Cheapest fare from Lille to Nice is 79€ and from Paris 43€. I assume the eurostar fare would be a little bit cheaper. I've carried a bike in a bag from the Gare du Nord to the Gare de Lyon and nearby stations, and to be honest I'd rather pay a bit more for the easier change. If you have an undismantled bike then cycling across Paris is dead easy.
- not many TGV trains to S of France take bikes (at the moment - it's improving)
Do you have any more information on that? I was thinking 'well that's good news' but then I looked on voyages-sncf.com for a sample day (2 May) and sadly I couldn't find
any services on the Paris-Nice line that had bike-carriage facilities (south-west France is another matter). Worryingly I also couldn't find the night train to Nice and Marseille that I referred to - even though I have a ticket for it for April (that may just mean that the tickets for the service haven't been released yet).