Is that "ha" as in he is laughing, or part of the Russian phrase?
No. It is not an English letter "h" it is a Russian letter "н" which is pronounced as "N".
Russian word "на" is a preposition.
Literally it reads:
На(To) ловца(the hunter) и(well / or hm / or you know) зверь(the prey / or animal) бежит(runs).