Question:  In France in 1852, voters were asked whether they approved of the re-establishment of the Empire in the person of Louis Napoléon Bonaparte,  the only president of what republic?

Context paragraphs:
French Second Empire referendum, 1852: A referendum on re-establishing the Empire was held in France on 21 and 22 November 1852.  Voters were asked whether they approved of the re-establishment of the Empire in the person of Louis Napoléon Bonaparte and family.  It was approved by 96.9% of voters with a 79.8% turnout.

Ecuadorian referendum, 1995: An eleven-part referendum was held in Ecuador on 26 November 1995.  Voters were asked whether they approved of the decentralisation of social and healthcare authorities, the privatisation of social security, equalising public spending between the provinces, abolishing civil servants' right to strike, whether the President should have the authority to dissolve the National Assembly, whether local councils should have a four-year term of office, whether the President and Vice-President of the National Assembly should only serve two-year terms, whether eight constitutional reforms proposed by President Sixto Durán Ballén should be approved, certain reforms to the judiciary, legal rights for civil servants and the creation of a Constitutional Court.  All eleven proposals were rejected.

French constitutional referendum, 1870: A constitutional referendum was held in France on 8 May 1870.  Voters were asked whether they approved of the liberal reforms made to the constitution since 1860 and passed by the Sénatus-consulte on 20 April 1870.  The changes were approved by 82.7% of voters with an 81.3% turnout.  However, France's defeat in the Franco-Prussian War caused the Empire to be abolished later that year.  Despite this being the ninth constitutional referendum in French history, it was the first to have more than 8% oppose the motion, and one of only four to have less than 99% official approval.

Australian republic referendum, 1999: The Australian republic referendum held on 6 November 1999 was a two-question referendum to amend the Constitution of Australia.  The first question asked whether Australia should become a republic with a President appointed by Parliament following a bi-partisan appointment model which had been approved by a half-elected, half-appointed Constitutional Convention held in Canberra in February 1998.  The second question, generally deemed to be far less important politically, asked whether Australia should alter the Constitution to insert a preamble.  For some years opinion polls had suggested that a majority of the electorate favoured a republic.  Nonetheless, the republic referendum was defeated due to division among republicans on the method proposed for selection of the president and dissident republicans subsequently supporting the no campaign.

French constitutional referendum, 1945: A constitutional referendum was held in France on 21 October 1945.  Voters were asked whether they approved of the Assembly elected on the same day serving as a Constituent Assembly, and whether until a new constitution was approved, the country would be governed according to a proposed set of laws that appeared on the ballot paper.  If the first proposal had not been approved, the Third Republic would have been restored, but its approval led to the creation of the Fourth Republic.  Both were approved by wide margins with a turnout of 79.8%.

French Constitution of 1852: The French Constitution of 1852 was enacted on 14 January 1852 by Charles Louis Napoléon Bonaparte (Napoleon III).  Slightly modified later that year, on 25 December 1852 the constitution became the basis for the creation of the French Second Empire.

Napoleon III: Louis-Napoléon Bonaparte (born Charles-Louis Napoléon Bonaparte; 20 April 1808 – 9 January 1873) was the President of France from 1848 to 1852 and, as Napoleon III, the Emperor of the French from 1852 to 1870.  He was the only president of the French Second Republic and the head of the Second French Empire.

French constitutional referendum, 1851: A referendum was held in France on 20 and 21 December 1851.  Voters were asked whether they approved of the continuation of the authority of Louis Napoléon Bonaparte and to delegate the powers required to produce a new constitution.  It was approved by 92% of voters with an 81.7% turnout.

Ecuadorian referendum, 1997: A fourteen-part referendum was held in Ecuador on 25 May 1997.  Voters were asked whether they approved of the dismissal of President Abdalá Bucaram by the National Congress, the appointment of Fabián Alarcón as interim President for twelve months, the calling of a Constitutional Assembly, whether a Constitutional Assembly should be elected by direct elections or by appointment, whether spending limits should be introduced for election campaigns, whether voters should be able to modify electoral lists, whether National Assembly elections should be held alongside the first or second round of presidential elections, whether political parties that fail to cross the 5% threshold in two consecutive elections should be deregistered, whether the Supreme Electoral Tribunal (TSE) should reflect the political makeup of the National Congress, whether the National Congress should appoint managers of state-owned companies with a two-thirds majority, reforms to the justice system, allowing the Supreme Court to appoint judicial authority member, whether elected officials who commit a criminal offence should be removed from office, and whether the National Assembly should implement the 13 proposals.  All eleven proposals were rejected.

French coup d'état of 1851: The French coup d'état of 2 December 1851 was a self-coup staged by Prince Louis-Napoléon Bonaparte (at the time President of the French Second Republic).  It ended in the successful dissolution of the French National Assembly and the subsequent re-establishment of the French Empire the next year.  When he faced the prospect of having to leave office in 1852, Louis-Napoléon (nephew of Napoléon Bonaparte) staged the coup in order to stay in office and implement his reform programs; these included the restoration of universal suffrage (previously abolished by the legislature).  His political measures, and the extension of his mandate for 10 years, were popularly endorsed by constitutional referendum.  A mere year later, the Prince-President reclaimed his uncle's throne as Emperor of the French under the regnal name Napoleon III.

Supporting paragraphs: French Second Empire referendum, 1852 Napoleon III
Answer: French Second Republic