* Hollande's first Turkey trip coincides with crackdown
* Erdogan criticised for purging police, judicial branch
* EU accession talks can go on, outcome unclear- Hollande
By Elizabeth Pineau
ANKARA, Jan 27 (Reuters) - French President Francois Hollande cautiously backed Turkey's aim to join the European Union on Monday despite its recent crackdown on police and judiciary and earlier French reservations about the idea.
In a long-planned state visit, the first by a French leader in 22 years, Hollande is seeking to mend frayed ties and smooth the way for French companies angling for contracts in Turkey.
But the visit has been overshadowed by Prime Minister Tayyip Erdogan's efforts to tighten controls on the court system in response to a corruption probe. European leaders criticised the AK Party leader in Brussels last week, saying democratic principles needed to be upheld.
Hollande said Turkey should continue to negotiate in view of joining the EU despite the criticism as such talks would allow it to address issues such as rule of law, judicial independence, separation of powers and respect of fundamental liberties.
"The (membership) process must be carried forward with the most difficult subjects, subjects that are necessarily the hardest," he said during a joint news conference with Turkish President Abdullah Gul, enumerating a series of negotiation points still to be covered.
Of 35 membership "chapters" to be checked off before Turkey can join the EU, 14 have so far been completed. If all the chapters are completed, France and Austria will put Turkey's EU membership to a referendum, as will the Turkish government.
"The negotiation process must allow Turkey to develop and show what it's capable of achieving... That is the answer that the Turks must provide," added Hollande.
Hollande's predecessor Nicolas Sarkozy favoured association status for Turkey over full accession, saying the country was too big, too poor and too culturally different to join the EU.
European Commission President Jose Manuel Barroso told Erdogan during the Turkish leader's first visit to Brussels in five years that respect for rule of law and independence of the judiciary were essential conditions for EU membership.
Gul, avoiding any mention of tension in Ankara except for two references to a "vigorous debate", said the negotiation was a technical process whose outcome would not be known until all outstanding issues had been laid to rest.
"We respect that the accession process is one to adopt legal and democratic criteria and judicial norms," he said. "We would not like this to become hostage to politics."
France and Turkey's relationship remains frayed two years after full diplomatic ties were restored after a falling out over a law which made it illegal to deny that the killing of Armenians by Ottoman Turks in 1915 was genocide.
Between 2009 and 2012, when France's Constitutional Court struck down the Armenian genocide law, French firms' share of foreign investment in Turkey shrank to 3 percent from 6 percent previously, French officials said.
Leaders of French infrastructure companies travelling with Hollande are eyeing Turkish markets for nuclear security and rail infrastructure expected to be worth $40 and $50 billion, respectively, by 2020, they added.
(Reporting By Elizabeth Pineau and Tulay Karadeniz; Writing by Nicholas Vinocur; Editing by Tom Heneghan)