Error: cURL could not retrieve the document, error 35

Yes :

In history log I have this kind of logs :

Event type Error log
Event time 12/03/16 18:30:18
Message Paypal: Error at notification received: could not reach Paypal gateway for notification check at www.sandbox.paypal.com . COMMUNICATION ERROR
Table affected Notifications
Table Key 362
Change
Change
Username System
Full name -
User Id 0
IP Address 173.0.82.126
Log Priority Error
Log Id 1921

And in Notifications this kind of messages (I replaced some confidential information by xxxxxxxxxx) :

Notification's details
Notification Id 362
IP Address xxxxxxxxxx
Notification type IPN payment gateway communication error
Log date 12/03/16 18:30:18
Username System
Full name System
User Id 0
Amounts and Currency
Currency EUR
Amount: single 10.00000
first
recurring
Tax
Shipping
Handling
Gateway fee 0.59000
Exchange rate
Settle amount
Settle currency
Payment Method and Transaction details
Payment method -
Gateway account
Type subscr_payment
Transaction id (txn_id) xxxxxxxxxx
Parent Transaction id
Sale id (sale_id)
Auth id
Payment date (as received) 08:45:04 Mar 12, 2016 PST
Payment type
Payment status Completed
Pending reason
Reason code
Test payment notification 1
Buyer details
First name test
Last name buyer
Company name
Address: Name test buyer
Address: Street Av. de la Pelouse, 87648672 Mayet
Address: City Paris
Address: State Alsace
Address: Zipcode 75002
Address: Country France
Address: Country code FR
Address confirmation status unconfirmed
Payer name
Email xxxxxxxxxx@xxxxxxxxxx.fr
Payer id xxxxxxxxxx
Payer status verified
Country of residence FR
Contact phone of payer
VAT number of payer
Seller details
Business id of receiving account xxxxxxxxxx@xxxxxxxxxx.fr
Email of receiving account xxxxxxxxxx@xxxxxxxxxx.fr
Payment Receiver id xxxxxxxxxx
Sale's details
Invoice number N72
Memo from payer
Item number S62-599-2
Payment basket 52
Notification's raw data
Raw result COMMUNICATION ERROR
Raw data $_GET=array (
'option' => 'com_comprofiler',
'view' => 'pluginclass',
'plugin' => 'cbpaidsubscriptions',
'cbpgacctno' => '1',
'cbppdtback' => 'xxxxxxxxxx',
'cbpbasket' => '52',
'result' => 'notify',
'cbpid' => 'xxxxxxxxxx',
'format' => 'raw',
'Itemid' => NULL,
'task' => 'pluginclass',
);
$_POST=array (
'mc_gross' => '10.00',
'invoice' => 'N72',
'protection_eligibility' => 'Eligible',
'address_status' => 'unconfirmed',
'payer_id' => 'xxxxxxxxxx',
'address_street' => 'Av. de la Pelouse, 87648672 Mayet',
'payment_date' => '08:45:04 Mar 12, 2016 PST',
'payment_status' => 'Completed',
'charset' => 'windows-1252',
'address_zip' => '75002',
'first_name' => 'test',
'mc_fee' => '0.59',
'address_country_code' => 'FR',
'address_name' => 'test buyer',
'notify_version' => '3.8',
'subscr_id' => 'xxxxxxxxxx',
'custom' => '52',
'payer_status' => 'verified',
'business' => 'xxxxxxxxxx@xxxxxxxxxx.fr',
'address_country' => 'France',
'address_city' => 'Paris',
'verify_sign' => 'xxxxxxxxxx',
'payer_email' => 'xxxxxxxxxx@xxxxxxxxxx.fr',
'txn_id' => 'xxxxxxxxxx',
'payment_type' => 'instant',
'last_name' => 'buyer',
'address_state' => 'Alsace',
'receiver_email' => 'xxxxxxxxxx@xxxxxxxxxx.fr',
'payment_fee' => '',
'receiver_id' => 'xxxxxxxxxx',
'txn_type' => 'subscr_payment',
'item_name' => 'Souscription pour xxxxxxxxxx',
'mc_currency' => 'EUR',
'item_number' => 'S62-599-2',
'residence_country' => 'FR',
'test_ipn' => '1',
'transaction_subject' => 'Souscription pour xxxxxxxxxx',
'payment_gross' => '',
'ipn_track_id' => 'xxxxxxxxxx',
);
$error='Error: cURL could not retrieve the document, error 35.';
$status='0';
$transaction_info='';

This error message reads to me like your webserver cannot reach Paypal.

This can be for a variety of reasons, most common one being a hoster that has a firewall not allowing outgoing https requests from your webserver to paypal!

I asked my hoster - they say there is no restriction on the firewall
curl is activated
If you have any other Idea of what I can look at , would be nice

Error 35 is an SSL error. Generally this means you're not able to make outbound SSL CURL calls.

curl.haxx.se/libcurl/c/libcurl-errors.html#CURLESSLCONNECTERROR

This is almost always a firewall issue, but could be a server configuration problem.

www.google.com/search?q=php+curl+ssl+connect+error+35

You may want to consider upgrading PHP to a new release (at minimum 5.4, ideally 5.5 or 5.6).