Well, right from the first scene of the movie, we have seen the whole theme was a joint investigation by the Russian MVD and American FBI. Now the rule is FBI is made to
to protect and defend the United States against terrorist and foreign intelligence threats, to uphold and enforce the criminal laws of the United States, and to provide leadership and criminal justice services to federal, state, municipal, and international agencies and partners. It performs these responsibilities in a way that is responsive to the needs of the public and faithful to the Constitution of the United States.
But to achieve that mission, they might need to want help from other countries. FBI
can not arrest a person in a soverign country but any country can allow them to cooperate FBI with their own forces in investigation and catching criminals. In Jackal, we have always seen Russian MVD have accompanied FBI in searching Jackal right from the very start and in Montreal also it continued. So the FBI was never alone. Rather it was a joint venture which is practical.
But one thing I would like to cite from FBIs official site:
How accurately is the FBI portrayed in books, television shows, and motion pictures?
To that faq it stated:
Any author, television script writer, or producer may consult with the FBI about closed cases or our operations, services, or history. However, there is no requirement that they do so, and the FBI does not edit or approve their work. Some authors, television programs, or motion picture producers offer reasonably accurate presentations of our responsibilities, investigations, and procedures in their story lines, while others present their own interpretations or introduce fictional events, persons, or places for dramatic effect.
Now make out something from it!