Fitzsimons was born in Ireland around 1741. By 1760 he had immigrated to Philadelphia, and began work as a clerk in a mercantile house. He married Catherine Meade on November 23, 1761 and formed a business partnership with her brother George. Their firm specialized in the West Indies trade, and would operate successfully for over 41 years.
As the Revolution neared, he supported the Whig position. Early in the Revolutionary War he served as captain of a company of home guards, but the only report of their actions was to support the regular troops for the Battle of Trenton in 1776. Later in the war he provided supplies, ships, and money in support of Pennsylvania’s forces.
Fitzsimons entered active politics as a delegate to the Continental Congress in 1782 and 1783. He was a member of Pennsylvania’s House of Representatives in 1786 and 1787. He was also a delegate to the U.S. Constitutional Convention in 1787. Although not a leading member of that convention, he did support a strong national government, opposed slavery, and favored giving the congress powers to tax import and exports, as well as granting the house and the senate equal power in making treaties. He was one of only two Catholic signers of the Constitution.
After the constitution was established, he served in the first three sessions of the House, finally failing to win re-election in 1794. He lost to upstart John Swanwick, who carried 7 of Philadelphia's 12 Districts and 57% of the vote. This was partially attributed, not to Fitzsimons's own fault but to public opinion turning against the Federalist Party, to which he belonged, in the wake of the Whisky Rebellion's suppression.
While withdrawing from politics, Fitzsimons remained active in civic and business affairs. He served as president of Philadelphia's Chamber of Commerce, as a trustee of the University of Pennsylvania, and a director of the Bank of North America. He was a founder of the bank, and supported efforts to found the College of Georgetown.