between each country

No, that is acceptable, and the more so as the first clause refers to country in the singular.

Thanks.

The entire sentence is mixed up. It should say:

"With countries having faith in one another, it will allow a closer bond between countries to help fix the problems occurring in Europe right now."

That still does not sound right, but I don't know what it was supposed to say. Specifically, "it" is not identified, and "faith" is not a term normally associated with countries.