NEW YORK—The dollar fell Tuesday after U.S. housing data for July came in well under expectations, further fueling doubts about the pace of the U.S. recovery. The franc hit a record high on the euro.

However, the euro reversed its recent slide against the dollar, but some other higher-yielding currencies such as the Canadian and Australian dollars were lower on the day. The U.S. currency fell against the yen, though it managed to pull back above its 15-year low, at 83.58 yen, hit in the immediate aftermath of the housing...