'cross our path' is correct and usable in written English.
It can be used to refer to an obstacle or an event in one's life that gets in the way. For example, "We have encountered many difficult challenges that have crossed our path on this journey."
Four wonderful destinations, 11 days of togetherness, thousands of photos, and one memory of a lifetime.. Some said that we don't meet by accident, they are meant to cross our path for a reason and ours is no exception.
"It's Isis saying to them: look what will happen to you if you cross our path.
Mostly we dawdle, catching the kudus and hartebeests, spotting a tawny eagle, and having a giggle as a herd of zebras cross our path.
On a rutted track we grope our way slowly along the shores of Lake Superior, as white-tailed deer cross our path.
We see that opportunities are everywhere, every day, and we make the most of those that cross our path.
We must see opportunity everywhere, every day and make the most of those that cross our path.
"It seemed very random that he should cross our paths there and then, at that moment," the campaigner said.
Would we feel the same when beautiful wild creatures cross our paths unexpectedly, as happened to my family this summer?
And if that rope is needed as a guideline for a ferry to a farther shore then one must invent a way to weave it back, or there will be drownings in the streams that cross our paths.
It was probably a different shop altogether, but the memory is a reminder of how closely human lives brush against each other in a big city, and how little we know about most of the people who cross our paths.
I think what makes more sense is learning to fish with the inevitable bears that will cross our paths.
