GM has bought a 7% share of PSA (Peugeot and Citroen). I don't see why they would. Back in the year 2000, GM bought 20% of Fiat, which was to save them both handsomely in financial terms. It didn't turn out to be that way, so GM decided to leave the alliance. To do so, GM had to pay Fiat $2bn to get out.
This time round, the venture is more limited in scope. Any real savings will take years to materialise. They will share engineering development and hope to launch the first common design in five years time. They will also combine purchasing and by 2017 they plan to save $2bn a year. GM Europe and PSA lose money in Europe, so that is an incentive to link arms.
It appears to be a cautious arrangement that may end up giving neither party that much. The good news is that even if that is the outcome, it shouldn't hurt either company either.