As far as I remember, mostly it was to survive against the onslaught of the rest of Europe. Most of the initial stage of the revolution was seen as an internal matter to France but some of the propaganda of the revolution was spread abroad. All the crowned heads of Europe were (rightly) worried about the events in France. So, spreading the revolution was seen as a way to make them worry about their own countries instead of attacking France. There was always a risk of Austria intervention (because of the Queen) which eventually lead to war.
George Lefebvre's The French Revolution, chapter 11 The Constituent Assembly and Europe has a full analysis of foreign relations at the time. This reference section contains may good sources.
Lafayette: Hero of the American Revolution by Gonzague Saint Bris has a large section on his role during that time and contains more about the relationship between France and the USA.