First, because of the softness of the soil, they have to support the foundations with piles. The actual foundation of the hippodrome can not be fit with the new one. 90 years ago it was ok but with new technologies and the weight of the new building and to match with the new foundations, they will have to install 1000 of those piles and it will last until next montrh of March. So they would have to dismantle that building anyway to install piles and build new foundation.
Second, in the actual case, they estimate to have finish dismantling the facade in 3 weeks, by just putting them down. Imagine the time it would take to dismantle it brick by brick to re-use them for the rebuilding of it. Coding, cleaning and storing them, changing the ones that have been installed during repairs when it cought on fire (just look at the 2 towers, lot of bricks lighters on the right side). Just try to realise the price and time just for that.
Third, try to match a building with view all around with an opac entrance with only 3 small doors and even smaller windows... Like mayor Labaume said: " If you want to build a crocodile, you build a crocodile. If you want to build a lion, you build a lion. But we won't build a crocolion! "