Paraguay's congress in June voted to impeach former President Fernando Lugo and installed Franco, Lugo's deputy, as president.
Lugo's fall followed political disturbances that he seemed unable to control but Unasur called it a coup. Lugo, who accepted the vote, later called it a "parliamentary coup."
Latin America's Mercosur trade bloc has also suspended Paraguay's membership but the Organization of American States announced it would wait for Paraguay's democratic transition next year.
Paraguay is worried its fragile economy, battered by recent outbreaks of farm animal disease, will suffer more as the country's suspension from two major regional groups begins to affect trade and political relations.
Franco indicated he wasn't concerned over Paraguay's suspension from Unasur, which he called a club of presidents, but was more interested in ascertaining OAS policy toward the country. The OAS has resisted calls by Mercosur and Unasur member-states to suspend Paraguay.
Federico also sent signals this week he wasn't going to fall for a populist backlash to Mercosur's controversial admission of Venezuela into the pact, demanded by politicians and some parts of Paraguayan media. Paraguay's congress was the last remaining hurdle to Venezuela's membership of Mercosur but that obstacle was removed when the country was suspended and excluded from regional consultations.
Paraguayan congress members had been opposing Venezuela's admission, arguing the radical policies of Venezuelan President Hugo Chavez would be too disruptive for Mercosur.
With Paraguay suspended from the group, the three other founding members, Argentina, Brazil and Uruguay secured speedy ratification of Venezuela's membership. Their move has been criticized as being profit-motivated.
Venezuela, a major oil producer with a small manufacturing base of its own, is a net importer of much of the merchandise exported by Argentina, Brazil and Uruguay.
The trio's tactic earned them few friends in Paraguay but Federico has indicated he's in no mood for retaliatory politics. He told Paraguayan congress members Venezuela's membership needs "a good in-depth analysis and no hasty decision."
Government analysts agree that a further deterioration in international relations between Asuncion and neighboring governments won't help Franco's aim of an early diplomatic rehabilitation of the country.
Paraguay's next general election is due to take place next April when the regional organizations will have few reasons to delay restoration its membership of Mercosur and Unasur.