Not quite. Starting from September 21st, most products (98 % of tariff lines) have indeed become free of duties thanks to the CETA, but some products are still subject to regulations.
To name just a few, clothing and textile products do require an import license and are subject to tariff quotas as per the rules of origin. The exporter must certify that the goods meet the origin requirements, which means that sufficient processing of the product must have taken place in the European country of manufacture. The Protocol on rules of origin states that “all exports under the origin quotas must make reference to Annex 5-A. The Parties shall not count any products against the annual origin quota without such reference.”
The importer also needs to obtain an import permit. This can be done by a broker on behalf of the importer. Import permits are issued per-shipment and on a “first come first served” basis. Permits are only issued if there is sufficient quota remaining, otherwise, the importer will pay the full tariff duty rate of 18%. The amount of quota remaining is published on the Government of Canada’s website and updated weekly.
The cost for an import permit is about $100 CAD. Note that there are only three lines on each permit and each article type requires a line. For example, 250 men’s woven cotton shirts, 150 ladies’ woven cotton shirts and 135 ladies’ woven polyester shirts would take up one permit. Additional types of articles would require additional permits, so for example twelve different articles would require four import permits, costing approximately $400. Note that it takes approximately 24 hours to obtain an import permit and all the shipment details are required in order to apply.  The importer must have an importer file number issued by the Government of Canada.
Concerning cheese, the CETA also allocates an import quota that allows some quantity to be imported free of customs duties. This quota should increase progressively in the coming years.
Be aware that negotiations are still ongoing on the topic of automobile importation. Therefore, some cars may still be subject to import restrictions. You may contact Transport Canada for more information on this subject.
Some other products are not fully free of customs duties as of now, but their tariffs will gradually decrease over the years. To check up the tariff duties on imports into Canada by product type, consult Canada Border Services Agency’s website. If you intend to export goods into a EU country, you may use the Government of Canada’s website to find your tariff rate.