French train giant Alstom SA has reached a preliminary deal to acquire Bombardier Inc.’s train business for more than $7 billion, according to people familiar with the matter, the latest effort by Alstom to gain scale amid the prospect of increased competition from China’s state-owned CRRC, the world’s largest rail supplier.

The deal is also the latest move by Canada’s Bombardier to dramatically shrink its business after production problems and order delays in its core train unit and rising costs in some of its aviation...