Yes there are public free beaches in Cannes even at the Croisette and they are as clean as the private beaches. As what concerns the crowd it all depends from the season and also of the time of the day.
The ones I saw were nice and not so crowded at the end of September even on a sunny Sunday afternoon. At the Croisette there is one near the Palais des Festivals if I remember well and a nicer one at the east end on the side of a public garden (photo 1 & 2). From this beach you have a view on all the Croisette, the bay of Cannes with the Lérins islands.
There are more free beaches west of the Vieux-Port at the Plage du Midi. There are a few private beaches with restaurants at the boulevard Jean Hibert but walking further west wards it's all free. Behind the sandy beach are the road and the railway once you have left the residential area with apartments around the square Mistral. (photos 3 & 4). The views on the Massif of the l'Estérel are very nice.
On the east side of Cannes there is also a free beach behind the Palm Beach casino. The view at this "Pointe de la Croisette" is very wide as you can see not only the whole Bay of Cannes but also the Golfe-Juan.
If it is your first stay on the Côte d'Azur you will see that "monokini" (topless) is still practised; after all it's here that it was invented in the sixties. It seemed to me that this mode is now declining. Is it a matter of dermatological risks or imported prudishness?
The beaches of Cannes have three main advantages: fine and clean sand, oriented to the South, nice views on the Lérins islands. Their main disadvantages are the crowd in festival and summer periods and the very high prices for the private beaches located at the Croisette.
The private beaches of Cannes are a profitable industry providing the usual beach beds and parasols as well as drinks and foods.
One should note that between the restaurant-bar area and the sea there is only 20 - 30 m of sand available for the clients.
If you like intimacy Cannes is not the place to go. If for you a pleasant beach is one where you will have no neighbours in a radius of at least 50 m you better avoid all the Côte d'Azur.
The lack of space is even so that on some private beaches they build platforms in the sea to allow VIP getting sunburnt not to close to each other.
Now if you like to socialize, these private beaches at the Croisette are among the best.
My photos taken from the promenade will give you an idea what it looked at the end of September which is a quiet period.
I just want to mention that West of the Vieux-Port you will find a fine sand beach called Plage du Midi with a very nice view on the "Massif de l'Estérel". Although the sand and the water are as good as on the Croisette beach they are less expensive because less chic and away of the famous hotels of the centre of Cannes.
The beach in Cannes is very good, compared to the one in Nice which is rocky, in Cannes you have smooth sand, the beach is large and you have a lot of options, from free area where you can land your towel to expensive private beaches in front on the hotels where you can't be seen from the promenade zipping exotic drinks and listening to soft music or just the surrounding sound of the sea and beach.
The beach at Cannes is one of the best in the entire region. For starters it actually has sand instead of rocks, whether they ship it in for the film festival or not I don't know but if your looking to build a sand castle with sand instead of rocks than the beach at Cannes is your best bet. Its along stretch of beach that has about average width, its crowded during the tourist season so get there early.
With its Mediterranean climate, Cannes offers near unbroken sunshine and warm temperatures throughout the summer making it ideal for a beach holiday. The city is equipped with three long (though not too wide) beach areas. The main beach is in the centre along boulevard de la Croisette. The second largest beach area is past le Vieux Port opposite Sofitel Hotel. The third is past le Palm Beach at the other end of Cannes (opposite Cap d'Antibes and îles de Lérins). In most of these areas, there are private beaches where one could rent a mattress and an umbrella (and have access to "room service"), or simply head to "la plage publique" with one's own towel and umbrella.
Cannes has a lot of private beaches owned by the large hotels and it's very expensive to lounge in th sun at these.On the other side of the Palais des Festivals thre is a small free beach that is very popular. On our last visit there were a few young men doing sand sculpture the exhibition was very good. Now thats something you'll never see in Nice!
We spent almost all our time in Cannes on the beach, with one hour in the sun for every five minutes in the water. In 35 degrees heat, there was no better way to pass the time!