这句英文有错吗

有错: listen--listens to 因为listen是不及物动物，必须与to搭配使用。
主语he为单三，故listen要加S。

causing -- makes/is making 因为that从句中需要谓动，
而causing 是非谓语动词，不能作谓动，又后面的不定式laugh没带to，
故将causing改为makes /is making

即: ...when he listens to a Russian joke...
...when he listens to a joke that makes/is making British laugh to tears.

For example,it is probablely hard to laugh when a Frenchman listens to a Russian joke. In the same way, it is improbable for a Russian to laugh when he listens to a joke that causing a Englishman laughs to tears

或者，我感觉这样写也可以：
For example,it is probablely hard to laugh when a Frenchman listens to a Russian joke. In the same way, it will cause an Englishman to laugh to tears while for the same joke a Russian may feel none of fun with it.

For example, It is very difficult for frenchmen to laugh when they hear out a Russian joke. The same reason, A joke can make Englishmen laugh to burst into tears, but Russian might fail to see anything amused.

我看下来。。没有错啊，兄弟。
正确的。

例如，它是不可能的，一个法国人会笑的时候，他听了俄罗斯的一个笑话。以同样的方式，它是一个俄罗斯会笑的时候，他听了一个笑话，使英国人笑出泪不可能。
你的这句是这个意思，应该是这么一句吧
A Frenchman, for instance, might find it hard to laugh at a Russian joke. In the same way, a Russian might fail to see anything amusing in a joke which would make an Englishman laugh to tears.