Jackson himself was never committed to universal manhood suffrage and at no point in his political career, whether as president or before, did he ever lift a finger in order to expand suffrage. In 1796, he supported suffrage restrictions while helping to draft Tennessee's Constitution. In 1822, he supported suffrage restrictions in Florida as territorial governor. During his administration, suffrage was entirely expanded by a state by state basis and I'm not aware of anything he did to support those efforts.
Is this including free Black men? I was always under the impression that Jackson was an important voice for expanding the vote to more White men, but obviously women and Blacks weren't a part of his vision.
No, by and large black men were not included in the vision of removing property qualifications for voting. In fact, in many cases, this was actively regressive for black men - for instance, in New York (an admittedly small number of) black men met the property requirements to vote and had that right restricted further (although not totally stripped away) in the 1821 Constitution, largely written by Martin Van Buren, which otherwise lifted property restrictions for white men.
Source (long PDF warning, it's a 34 page paper from Albany Law School on the history of black suffrage in New York, relevant section starts on page 9 of the document)
