Network Preferences says I’m connected but I am not

What does Wireless Diagnostics show?

Wireless Diagnostics

Wi-FI connection drops

Wi-Fi Problems in OS X Yosemite

Wi-Fi Problems in OS X Yosemite (3)

WiFi Potential Temporary fix - Yosemite 

Also try turning off Bluetooth.

If your Wi-Fi source is capable of generating a 5 GHz Wi-Fi network, try that to help avoid conflicts with Bluetooth.

Sys Prefs>Network Pref Pane, highlight Interface>Advanced button>DNS tab>little + icon.

 Try putting these numbers in...

8.8.8.8

8.8.4.4

Apply.

Reboot the computer.

Reboot the modem.

Reboot the router and test.

How to troubleshoot Wi-Fi connectivity_apple support

Great news Pierre, thanks for the report. :)