* Third-quarter core profit down 0.7%

* Adds customers in Spain and France

* Reiterates full-year targets

PARIS, Oct 26 (Reuters) - French telecoms operator Orange's quarterly profit was hit by lower returns from co-financing deals to deploy networks, it said on Tuesday.

Like other European operators, the state-controlled former monopoly struggles to maintain strong upward momentum in earnings, caught between the need to upgrade networks while contending with fierce competition in France and Spain, its biggest markets.

Third-quarter earnings before interest, tax, depreciation and amortisation after leases (EBITDAaL) dropped by 0.7% from a year earlier to 3.55 billion euros ($4.13 billion) despite increasing customer numbers in France and Spain.

Orange has signed deals with French rivals such as Bouygues Telecom and Iliad's Free to help it to deploy broadband fibre networks, adding revenue to the group's regular sale of mobile and broadband contracts.

Under such co-financing deals, Orange receives payments from rivals in exchange of the right to use the networks.

Lower returns from these deals explains a 4.1% drop in Orange's sales in France, Chief Financial Officer Ramon Fernandez told reporters.

Over the July to September period, Orange managed to add 121,000 customers for its mobile business in France, plus 80,000 new broadband customers.

It also added new clients for both businesses in Spain, where it took a 3.7 billion euro writedown in the second quarter to reflect the market's decreasing value.

Orange reiterated its full-year targets, including a slight decline in core operating profit and underlying cash flow from telecoms activities of more than 2.2 billion euros, down from 2.5 billion euros in 2020.

It also reiterated its targets for 2023, which include underlying cash flow from telecom activities of 3.5 billion to 4 billion euros.

Orange Chief Executive Stephane Richard has told French weekly JDD he would be willing to stay on as group chairman when his third four-year mandate as CEO ends in May 2022. ($1 = 0.8593 euros) (Reporting by Mathieu Rosemain Editing by Sudip Kar-Gupta & Shri Navaratnam)