He kept his head otherwise the accident would have happen

是would have happened.
情态动词过去时 + 完成时表示对过去事情的推测.这里也是一样..表示推测"要不是他kept his head,就会发生一场事故"...例如:
I would have done my homework if I wasn't ill.如果不是我病了,我已经做完作业了...
类似的还有:
must have done/ could have done/should have done等等...详细信息请参见语法书上对表推测情况的说明..

原句绝对有错。
应用WOULD HAVE HAPPENED
另外我觉得前面也有错，KEPT HIS HEAD后面应该还有个副词。
回答完毕。
P。S。过去将来时是这么用的吗？！楼上不要乱讲。再说这也不是过去将来时。是虚拟语气，虚拟过去。

他保持头脑清醒 否则就会发生事故

因为这个事故还没有发生，使用过去将来时。来表现通过kept his head 这个动作才能使事故不发生。